However, Bowen's late winner marks a first-ever major honour for David Moyes in management, and West Ham's first as a club since 1980.
Fiorentina have now lost their last four European finals, with their last coming back in 1990, and Vincenzo Italiano's side have been defeated in two major finals this season, following defeat to Inter Milan in the Coppa Italia.
Both managers made surprise omissions to their starting lineups, with Italiano opting to leave Conference League joint-top scorer Arthur Cabral on the bench for Luka Jovic, while also choosing Christian Kouame over Jonathan Ikone.
However, La Viola would then go on to control proceedings in the opening 45 minutes, and had their first sighter when Rolando Mandragora fired wide from a long-range effort inside 10 minutes.
Cristiano Biraghi's left-footed deliveries were always likely to be a factor, and it was his dangerous corner that presented Nikola Milenkovic with an opportunity soon after, but the Serbian headed over.
It was from another Biraghi corner where the first-half's big flash point came, when plastic cups and lighters rained down from the West Ham supporters, with one of the missiles striking the left-back on the head, causing a very nasty cut and excessive bleeding.
Just seconds earlier, Nicolas Gonzalez managed to catch a cup preventing it from striking him in the face, and the female assistant on that side was struck in the leg by a stray throw.
The referee stopped the game momentarily, speaking to both teams and his fourth official while Biraghi's gashed head was treated, and the West Ham supporters were warned over the tannoy.
Back on the field, West Ham mainly had to rely on set pieces for any chances in the first half, as Declan Rice failed to test Terracciano with Fiorentina struggling to clear from a long throw, before the England midfielder had another effort blocked after Kouame miskicked his clearance from a corner.
Deep into the extended stoppage time caused by the crowd trouble, the Serie A side thought they had taken the lead when Kouame's header bounced off the post, falling nicely for Jovic who bundled the ball home, before being denied by the linesman's flag.
For all of Fiorentina's first-half territorial dominance though, on the hour mark, West Ham were presented with a golden chance to take the lead in the final after Biraghi was penalised for a handball in the box following a VAR check.
Benrahma, who had been quiet all evening until that point, was clinical from the spot, sending Terracciano the wrong way to give the Hammers a priceless lead.
However, the jubilant celebrations saw the Algerian potentially fortunate not to receive a second yellow card after jumping in the crowd, as the winger was booked for diving in the first half.
Moyes's side took control in the immediate aftermath of the goal, but on the break from a long ball, substitute Cabral was denied by an excellent block by Kehrer, who himself had not long come off the bench.
With the Hammers support in full voice, they were soon silenced, as Bonaventura's superb close control from Gonzalez's knock down opened up half a yard of space and the experienced midfielder found the far corner beyond Alphonse Areola.
The game turned into one more accustomed to how Fiorentina have played under Italiano, as their perceived gung-ho approach saw the game burst into life.
Antonio was played through at one end and missed one-on-one before being flagged offside, and just seconds later, Mandragora flashed a shot wide for Fiorentina after some good hold-up play by Cabral.
Fiorentina began to look leggy late on though, and with just seconds left of the 90, Paqueta's through ball caught La Viola's defence flat-footed, and Bowen held his nerve to beat Terracciano one-on-one to seal a historic victory.
Despite playing almost eight minutes of added time, West Ham hung on, sparking ecstatic scenes from the fans in claret and blue, with the Hammers crowned the second-ever Europa Conference League champions.No Data Analysis info