The victory also provided an immediate boost for returning head coach Paolo Vanoli, who was back in the Fiorentina dugout following the dismissal of Fabio Grosso after the club's difficult start to the campaign.
• Venezia: Akor Adams 22', Antoine Hainaut 86'
• Fiorentina: Franco Mastantuono 29', 30', 84', Mateo Pellegrino 66'
Venezia started brightly and took the lead in the 22nd minute. Gianluca Busio won possession and released Akor Adams, who cut inside before firing a precise right-footed shot beyond David de Gea.
Fiorentina's response was emphatic.
Just seven minutes after falling behind, Mastantuono produced the first of his three goals. Álex Jiménez found the Argentine on the right, and the teenager cut inside before firing a low left-footed effort from outside the area that beat Filip Stanković.
Barely a minute later, Mastantuono struck again. Beto's pressure forced a defensive error, allowing the forward to collect the ball and fire another low effort into the corner to complete a remarkable turnaround before half-time.
Venezia dominated possession for periods after the break as they searched for an equaliser, but Fiorentina remained dangerous on the counter.
The visitors extended their advantage in the 66th minute when Nicolò Fagioli released Mateo Pellegrino into space. The Argentine forward raced clear and calmly finished into the bottom corner to make it 3–1.
Mastantuono then completed his hat-trick in the 84th minute. The youngster's initial close-range effort was saved by Stanković, but the ball rebounded off him and fell perfectly for the forward to finish from close range.
Venezia responded almost immediately when Antoine Hainaut volleyed home from Ridgeciano Haps' cross in the 86th minute, but the hosts could not find a third goal as Fiorentina held on for a valuable victory.
The result lifted Fiorentina from the bottom of the Serie A table and gave them their first league points of the campaign after three successive defeats against Roma, Frosinone and Torino. Venezia, meanwhile, remain without a point after four matches.
For Mastantuono, the night was particularly memorable. His hat-trick made him the youngest Fiorentina player to score three goals in a Serie A match, underlining the significance of the 17-year-old's performance.
Vanoli could hardly have asked for a better return to the Fiorentina bench, while the emphatic comeback gives the Viola renewed confidence ahead of their next fixtures.