Bowen raced onto a through ball from Lucas Paqueta to secure a 2-1 victory in the last minute of normal time at the Eden Arena, after Giacomo Bonaventura had cancelled out Said Benrahma’s penalty.
And Bowen’s goal ended West Ham’s 43-year wait for a major trophy, while securing a place in the group stage of the Europa League next season.
“I obviously dreamed of scoring, but to score the winner in the last minute,” he told BT Sport.
“It’s what you always say, you want to score a last-minute winner and to do it in front of these fans, I thought I was going to cry, I’m just so happy.
“I can’t put it into words, we’ve had a dream, we haven’t had the best season, myself included, but to do what we’ve done tonight, for these fans, we said before, to give them this moment, I’m over the moon.”
The Hammers, having seen captain Declan Rice fire an early chance wide of the left-hand post, had a let-off on the stroke of half-time when a header from Luka Jovic was ruled out by VAR.
And they took the lead just past the hour mark when Bowen chested down Vladimir Coufal’s quick throw and saw the ball brush the knuckles of Fiorentina captain Cristiano Biraghi, who needed his head bandaged in the first half after being left with a cut from a plastic pint glass thrown from the crowd by a West Ham supporter.
Referee Carlos Del Cerro Grande pointed to the penalty spot after consulting a pitchside monitor and Benrahma dispatched his penalty confidently.
But Bonaventura angled a drive inside the far post when Nicolas Gonzalez nodded down a cross from the left to level soon after.
Extra time was looming when Paqueta pounced in the centre circle to thread a pass into space for Bowen to chase and he kept his cool to clip it over the leg of Pietro Terracciano and into the net for the most important goal of his career.
“In my position you make that run 10 times, and you might get it once, and soon as you get it you’ve got to put it away,” added Bowen.
“I had a lot of time but I was confident, and then I see it go in and I didn’t know what to do.”
It took Bowen’s tally to 40 goals in 158 appearances for the Hammers and he was ready to celebrate.
“I said leading up to this, this is the biggest game of my career,” he said.
“The emotion, I thought it was going to go to extra time and then there was time for one more chance and I’m just so happy.
“Look at everyone, it means so much. I want to celebrate with my teammates, these fans, my dad, my brother and two mates are on the front row, so for them to see it [is so special].”
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