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The home side looked the stronger from the start as Alberto Gilardino had an effort blocked just a couple of minutes after kickoff, while Josip Ilicic missed the target inside the opening five minutes.
Ilicic was on target inside the first 15 minutes, though, as Mohamed Salah raced down the flank before crossing in to the midfielder's path, leaving him with a simple tap-in.
He could have completed a first-half brace when Dario Dainelli gave away a free kick on the edge of the box midway through the opening spell, but his set piece was a touch high.
Federico Bernardeschi thought that he had doubled Fiorentina's lead just a couple of minutes into the second half as he coolly slotted the ball in after finding himself unmarked in the box, but his strike was ruled out for offside.
Ilicic continued to look lively in front of goal as he attempted to curl the ball in from the edge of the box, but his effort could not get the better of Albano Bizzarri.
The visitors started to see more of the ball as the match headed into the final half an hour, with Sergio Pellissier forcing a stop from Ciprian Tatarusanu, before striking the post with a venomous volley.
Chievo's hopes of getting back on level terms were dealt a blow with 20 minutes remaining, though, as Isaac Cofie picked up a second booking, leaving the visitors a man short for the rest of the match.
It did not take Fiorentina long to make the most of their numerical advantage, with Matias Fernandez forcing a parry with a low effort, leaving Bernardeschi to pounce on the loose ball.
Chievo were punished further in stoppage time as Milan Badelj collected a Bernardeschi pass on the edge of the box before smashing it into the bottom right corner, sealing a comfortable victory for the hosts.
With Napoli losing their final match of season, Fiorentina climb up to fourth in the final table, while Chievo finish 14th.