Bostjan Cesar fired the hosts in front at Stadio Marc'Antonio Bentegodi but two goals from Juan Cuadrado turned the result around for the Viola.
The win sees Fiorentina consolidate their place in the top six and provides a further boost to confidence following victories over Juventus and Romanian side Pandurii in the last seven days.
Chievo came into the match on the back of four successive defeats and are rooted to the foot of the table.
However, they showed promise in the early stages with Alberto Paloschi firing narrowly wide and Cyril Thereau forcing a save from visiting goalkeeper Neto.
And they took a deserved lead in the 14th minute thanks to Cesar, who was left unmarked to convert the easiest of headers following Boukari Drame's cross.
Question marks hung over Fiorentina's players, who looked as if their midweek European exertions may be taking their toll in Verona.
However, any doubts were dispelled a minute before the interval when Cuadrado produced a moment of magic to dart into the box and slot home into the bottom-right corner.
The Viola appeared rejuvenated after half-time as first Manuel Pasqual and then Borja Valero fired over the crossbar.
Marcelo Estigarribia should have restored Chievo's lead after 64 minutes but failed to make the most of some hapless Fiorentina defending by poking a shot from close range wide of the mark.
And the visitors took full advantage immediately as Giuseppe Rossi led a counter-attack before passing to Cuadrado for a simple tap-in.
Chievo tried to hit back but Thereau could only drive over from 25 yards.
And it was Fiorentina who came closest to adding to their tally with Cuadrado denied a late hat-trick thanks to a fantastic diving save from Christian Puggioni.