What We Learned From Week 8 in the N.F.L.

They’ve been banging at the Super Bowl door for half a decade. They’ve had their collective hearts ripped out in new inconceivable ways each January.

Could 2021 be the year the New Orleans Saints break through again? A 36-27 win over the defending-champion Tampa Bay Buccaneers must fill this injury-ravaged team with belief that it can be.

When the starting quarterback Jameis Winston was carted off the field with a knee injury early in the second quarter, and with the backup Taysom Hill still out with a concussion, the Saints had every reason to fold. Instead, they took Tom Brady’s best shots, keeping pace deep into the fourth quarter behind the journeyman Trevor Siemian until the defense came up with a game-saving play.

The New Orleans Saints won’t relent.

The drama at the Superdome truly started with 5 minutes, 44 seconds left in the fourth quarter, when Brady rainbowed a 50-yard touchdown to a wide-open Cyril Grayson. With three Bucs receivers lined up to the right, two Saints defenders bit on Mike Evans’s route underneath to leave Grayson all alone deep.

Brady has been throwing touchdowns to receivers nobody has ever heard of for a good two decades and Grayson kept that streak alive. Grayson was an All-American track sprinter at Louisiana State University, where he did not even play football. He has bounced around the league with eight different teams since 2017.

Grayson, a Louisiana native, caught his second career reception and first career touchdown to put the Bucs up, 27-26.

Yet, the Saints didn’t flinch.

Siemian drove the offense 70 yards in 12 plays to go back up, 29-27, on a 23-yard field goal by Brian Johnson (the third kicker the Saints have tried this season). Granted, Saints Coach Sean Payton’s clock management at the tail end of the drive was ugly. With incompletions on first and second down from Tampa Bay’s 9-yard line instead of running the clock, the Saints appeared to gift Brady 1:41 on the ensuing possession. With a timeout.

It didn’t matter. After Brady attempted a deep shot for Evans on the Bucs’ first play from scrimmage, Saints cornerback P.J. Williams stepped in front of Brady’s next pass for a pick and returned it for a 40-yard touchdown.

That’s the story of the Saints. Long gone are the days of their offense exploding for 350 passing yards each week. Rather, Payton has squeezed out as much talent as he possibly can from every crevice of the roster, and when the offense cannot find a playmaker, a defense built by coordinator Dennis Allen steps up.

The team’s lone star on offense, running back Alvin Kamara, was held in check, managing only 3.2 yards per carry and 76 total yards. Siemian threw his first touchdown pass since 2017 in the second quarter, but looked like a career backup thereafter.

Receiver Deonte Harris, playing in his first game since Week 5, fielded a key punt return and he and Marquez Callaway came up with clutch catches. The defense kept coming up with plays, an interception or a forced fumble, goading Brady into three turnovers. The Saints committed none.

The Saints are now 5-2 and thinking big yet again, while hoping to have their quarterback healthy to face Brady and the Bucs when it really counts: in January.

When his offense sputters, Josh Allen can flip a switch.

For two decades, the two franchises toiled in the same misery. The Buffalo Bills and the Miami Dolphins were essentially locked in Tom Brady’s A.F.C. East torture chamber.

After 17 division titles, nine conference titles and six Super Bowl triumphs as quarterback of the New England Patriots, Brady headed south to the Tampa Bay Buccaneers and a door cracked open for these two rivals.

The Bills gambled on the strong-armed quarterback few watched at Wyoming, Josh Allen, and then handed him a six-year, $258 million contract extension.

The Dolphins took the Alabama quarterback everyone saw in college: Tua Tagovailoa.

Now, it sure looks like the Bills will own the Dolphins, and maybe the rest of the division, for a while to come. The Bills’ 26-11 victory was their seventh in a row over the Dolphins, and the massive discrepancy at quarterback between the franchises is a major reason.

The game was unexpectedly tight through the first three quarters, with Buffalo’s typical pyrotechnics stalled by sloppy plays. Only one of the Bills’ first six drives traveled farther than 23 yards, and the score was tied, 3-3, at halftime.

One play with under a minute remaining at the end of the first half was particularly ghastly. On fourth-and-4 from Miami’s 44-yard line, Allen thought the Dolphins had jumped offsides and haphazardly pointed to the line of scrimmage while backpedaling midplay. He was hit, threw incomplete and then was flagged for intentional grounding.

Of course, the Dolphins’ popgun offense did nothing with this gifted field position, and fumbled the ball right back to Buffalo.

In the second half, Allen eventually overwhelmed Miami through sheer physical ability. As if sick and tired of this pillow fight, he dissected the Dolphins’ secondary on the Bills’ second possession of the half — a 13-play, 80-yard touchdown drive that ate up 7 minutes 6 seconds of game clock.

Allen hit receiver Cole Beasley for four completions on the drive alone, including a 15-yard floater on third-and-14.

On third-and-1, the 6-foot-5, 247-pound Allen bulled his way through the arms of Dolphins linebacker Elandon Roberts to gain 5 yards.

The go-ahead touchdown pass showed the sort of toughness and improvisation Allen makes look so, so routine.

On first-and-goal, and his face mask ripped sideways by the 266-pound defensive end Jaelan Phillips, Allen shook free and flipped an 8-yard touchdown pass to a wide-open Gabriel Davis. Impressive as the throw seemed then, replays confirmed that it had been a no-look pass, to boot.

On Sunday, Allen looked like Ben Roethlisberger in his prime — only stronger, faster and with a ton more attitude, resuscitating plays with the sort of confidence in his arm that all teams seek at the position.

Buffalo’s next drive ended with a 19-yard scoring strike to wideout Stefon Diggs, who promptly punted the football into the stands. The afternoon was capped by Allen’s third-and-6 touchdown dash into the end zone, the 28th rushing touchdown of his career.

He flexed his biceps. He snarled. He even mixed it up with Dolphins defensive tackle Christian Wilkins after a failed 2-point conversion attempt. When the two were separated by officials, Allen waved goodbye to Wilkins for seven seconds as he walked back to the Bills’ sideline.

Allen has done more than resurrected a franchise that has waited decades to get out of Brady’s Patriots shadow. With his refusal to back down, he has given fans a rallying point, an embodiment of their confidence.

While there may be questions about Patrick Mahomes’s recklessness at Kansas City, Baker Mayfield’s health at Cleveland and imbalances at Las Vegas, Baltimore and Tennessee, there is certitude in Western New York.

Wide receivers should stay close to their phones Tuesday.

N.F.L. teams have come around on roster building, realizing that clinging to draft capital forever rarely pays off. Contenders like the Los Angeles Rams have proven that the smarter play is often to go all in on proven commodities.

With the trade deadline on Tuesday, a handful of wide receivers should be available.

Allen Robinson has been thwarted by bad quarterback play and bad play-calling for most of his eight-year career, yet has found a way to churn out numbers. His relationship with the Chicago Bears was severely damaged before this season began when the two parties could not agree on a contract extension and Robinson accepted the franchise tag. Chicago’s 33-22 loss to the San Francisco 49ers on Sunday, despite a heroic outing from Justin Fields, should render the Bears (3-5) sellers at this deadline.

Elsewhere, Cleveland dropped to 4-4 with a 15-10 loss to the Pittsburgh Steelers, further proof that the Odell Beckham Jr.-Baker Mayfield marriage never worked for the Browns. Miami’s DeVante Parker and the Giants’ Darius Slayton, who is due only the rest of his $850,000 salary, should warrant interest, though the receiver who perhaps most wants a relocation, the Houston Texans’ Brandin Cooks, may stay put. After the Texans shipped Mark Ingram to the New Orleans Saints last week, Cooks voiced his frustration at the team’s direction.

Who could bite on adding a playmaking receiver? The Baltimore Ravens (5-2) and the Kansas City Chiefs (3-4) perhaps.

This season has been miserable for Patrick Mahomes, who has exhausted Tyreek Hill and Travis Kelce trying to compensate for a paltry defense. Trading for a receiver would put the team all in on outgunning opponents.

Lamar Jackson has been transcendent for the Ravens, but with receiver Sammy Watkins nursing a hamstring injury and a rotating cast at running back, Baltimore could use another option so Jackson does not have to take on too much of the load.

Around the N.F.L.

Patriots 27, Chargers 24: Maybe those close losses to Tampa Bay and Dallas will end up costing the Patriots, but Sunday was further proof that Coach Bill Belichick’s defense will always give this team a chance. Justin Herbert threw nearly as many incompletions (17) as completions (18) and had two passes picked off by Patriots safety Adrian Phillips, who returned one for a fourth-quarter touchdown. Next up for New England: three extremely winnable games against Carolina, Cleveland and Atlanta.

Seahawks 31, Jaguars 7: Jacksonville was flagged for having 12 men on the field on back-to-back plays, a befuddling pair of penalties with extra time to prepare given their bye last week. That just about summarizes how Urban Meyer’s first year as an N.F.L. head coach is going.

Broncos 17, Washington Football Team 10: Broncos safety Justin Simmons continues to be one of the best players we don’t talk nearly enough about. He smacked Washington tight end Ricky Seals-Jones to force one incompletion on a fourth-and-1, picked off two passes and had seven solo tackles. The Broncos’ defense gives them a chance in most games.

Panthers 19, Falcons 13: Carolina stopped the bleeding of a four-game losing streak with 203 rushing yards. After being benched in Week 7, Panthers quarterback Sam Darnold left this week’s game in the fourth quarter with a concussion.

49ers 33, Bears 22: Neither team looks like a contender, but Deebo Samuel got some recognition. He pulled off a 83-yard catch and run, and his 819 receiving yards through seven games breaks Jerry Rice’s franchise record of 781 yards set in 1986.

Titans 34, Colts 31 (overtime): After throwing one interception through Indianapolis’s first seven games, quarterback Carson Wentz threw two in the final eight minutes on Sunday. Tennessee capitalized to gain distance on the Colts, its only threat in the A.F.C. South.

Rams 38, Texans 22: Ho-hum. It was another massive day from Rams receiver Cooper Kupp, who helped the Rams race to a 38-0 lead through three quarters with 115 yards and a touchdown. It was his fifth 100-yard game of the season.

Steelers 15, Browns 10: It is scientifically impossible for a Mike Tomlin-coached team to die off in October. Ben Roethlisberger continued to own the Browns, even as a shell of his former self, with 266 yards, one touchdown and, most important, no turnovers.

Jets 34, Bengals 31: In his first N.F.L. start, the Jets backup Mike White outplayed the sizzling Joe Burrow, throwing for 405 yards and three touchdowns on a remarkable 37-of-45 passing. Four Jets players caught at least five receptions, and Bengals receiver Ja’Marr Chase (three catches on nine targets) was neutralized.

Eagles 44, Lions 6: Philadelphia fans had been clamoring for Coach Nick Sirianni to run the ball. Against the winless Lions, they got their wish. Quarterback Jalen Hurts threw only 14 times as a host of backs bashed away for 236 yards and four touchdowns on a combined 46 rush attempts. At 3-5, though, the Eagles should probably be sellers at the trade deadline.