But the hosts maintained their unbeaten start to the league season with an acrobatic equaliser from Estebian Cambiasso after Norberto Neto made a mess of a corner.
Inter sealed victory when full-back Jonathan collected Ricky Alvarez’s pass and lashed home his shot into the roof of the net eight minutes from time.
The game began well with both sides looking impressive on the counter attack.
Yuto Nagatomo produced the game’s first chance when he cut inside and fired a shot from distance which Neto saved. Minutes later, Saphir Taider could only find the side netting after a devastating counter attack.
Joaquin was the star man for the Viola after setting up striker Rossi whose low shot was parried, before the Italian turned provider to find the winger whose shot was saved by Samir Handanovic at his near post.
Ex-Manchester United striker Rossi carved out another opening on the half-hour mark but scuffed his shot wide from 25 yards out.
But it was Inter who ended the half more strongly with the impressive Nagotomo’s inviting cross from the left finding Fredy Guarin, whose shot against the ground was saved by Neto.
Guarin continued to impress and his rasping effort in the second half from 25 yards out was well saved by Neto.
But the deadlock was broken in the 59th minute when Juan tugged back Joaquin in the box to concede a penalty. Rossi fired home his spot-kick for his fifth goal of the season.
Inter brought on Mateo Kovacic and Mauro Icardi and turned the game around in a devastating 11-minute spell.
Neto missed Alvarez’s corner and Hugo Campagnaro flicked the ball on for Cambiasso to produce an acrobatic effort from close range to equalise on 71 minutes. It was the Argentine’s sixth goal in 18 games against the Viola.
Eleven minutes later, the hosts sealed victory when Alvarez’s scooped pass was controlled by Jonathan and the Brazilian lashed his shot into the roof of the net to cap off an impressive performance.
Sub Alvaro Pereira could have made it three in the closing stages when he was through on goal but his lethal effort was pushed over the bar by Neto.
Fiorentina had a final effort in stoppage time when Massimo Ambrosini jabbed his shot towards goal but Handanovic kept the ball out by diving low to his left as Inter clung on for victory.