Goals from Riccardo Sottil, Andrea Belotti and Nzola saw the hosts take the lead on three separate occasions after being pegged back by equalisers from Hans Vanaken and Igor Thiago following the initial two.
The visitors had gone down to 10 men just moments before their second goal after Raphael Onyedika's two yellow cards in a matter of minutes, allowing Fiorentina to take control of the remainder of the game and eventually find the winning goal in stoppage time.
Nzola's winner saw the hosts finally break Club Brugge's defence and secure a brilliant lead to take to Belgium for the second leg next week.
The game kicked off in the best possible way for the hosts as Sottil found himself in possession on the edge of the box, cutting onto his right foot and curling a sublime effort into the top right corner to put his side 1-0 up within five minutes.
The lead was not held for long though, as Club Brugge levelled just 12 minutes later through Vanaken's controversial penalty, being awarded after Thiago's initial strike was saved and the following loose ball struck Cristiano Biraghi's arm.
More to follow.