Vincenzo Montella nearly paid the price for resting several key men as his side scraped through on Thursday evening
Vincenzo Montella chose to rest Giuseppe Rossi, Massimo Ambrosini and Alberto Aquilani, a decision which almost backfired on the Tuscany outfit.
The Swiss visitors looked eager to bounce back from their 2-1 defeat in the first leg and troubled the Viola defence on regular occasions during the opening stages of the encounter.
Early on, Daniel Pavlovic tried to set Anatole Ngamukol free on goal with a through ball, but he was caught offside, and shortly after Shkelzen Gashi saw his header fly over the bar.
The hosts slowly began to wake from their slumber and efforts by Joaquín and Juan Guillermo Cuadrado were blocked by the Swiss defence.
But in the 38th minute, Michael Skibbe's men had a great chance to take the lead, when Vero Salatic picked up a headed a Shkelzen Gashi cross goalwards only to be denied by an excellent safe by Neto.
It was not until the 41st minute that the deadlock was finally broken, as Nassim Ben Khalifa blasted the ball into the bottom right corner to put the visitors ahead.
Nerves began to jangle amongst the home support at Stadio Artemio Franchi, as the Italians had only their away goal advantage left to hold on to and the second half proved to be a true test of the Serie A side's composure.
Montella had seen enough at this point and brought on Josip Ilicic for Juan Guillermo Cuadrado at the interval to add an extra cutting edge to his attack.
But it was the visitors who continued to look the most likely to score again, with Izet Hajrovic, who replaced Shkelzen Gashi late into the game, narrowly missing a good opportunity from the edge of the box.
The 22-year-old continued to threaten the Fiorentina backline and saw another effort from outside the penalty area just veer wide of Neto's top corner in the dying minutes of the match.
And the Viola held on to progress to the Europa League group stage on away goals, to leave Montella a relieved man at the full-time whistle.