Said Benrahma had opened the scoring on the hour mark with a penalty following a handball from Fiorentina's Cristiano Biraghi.
Giacomo Bionaventura then equalised five minutes later before Bowen's sensational late winner.
The Hammers then had to endure over eight minutes of stoppage time after just five was shown on the fourth official's board.
The first half, however, was marred by objects being thrown by West Ham fans onto the pitch – one of which struck Biraghi and caused a head wound.
It is the first major trophy of David Moyes' managerial career, which started 25 years ago with Preston.
West Ham started their Europa Conference League campaign ten months ago, in qualifiers against Danish side Viborg. After comfortably navigating their way through the two-legged tie, they were then drawn in a group with Romanian team FCSB, Silkeborg from Denmark and Anderlecht.
In the knockout stages, they then beat AEK Larnaca, Gent and AZ Alkmaar en route to the final.
Previously the winners of the Cup Winners' Cup in 1965 and the Intertoto Cup in 1999, West Ham have now added the Europa Conference League to their European trophies honours list.
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Conor Pope is the former Online Editor of FourFourTwo, overseeing all digital content. He plays football regularly, and has a large, discerning and ever-growing collection of football shirts from around the world.
He supports Blackburn Rovers and holds a season ticket with south London non-league side Dulwich Hamlet. His main football passions include Tugay, the San Siro and only using a winter ball when it snows.