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Mario Gomez then directed a header narrowly over the bar, before nodding another effort wide minutes later.
Fiorentina gradually took control of the game and Manuel Pasqual was picked out at the back post, but could only volley straight at the keeper.
At the start of the second half Alberto Paloschi had the ball in the net for Chievo, but his effort was ruled out for offside.
The hosts continued to press for an equaliser and in the 72nd minute Sergio Pellissier made the most of some slack defending to fire in at the back post.
Soon after, Matias Fernandez came close to restoring Fiorentina's lead with a powerful strike from the edge of the box that was touched behind by the keeper.
With the game heading towards a draw, the visitors stole all three points deep into stoppage time as substitute Babacar headed in Joaquin's cross, leaving Chievo no time to mount a response.