Manuel Pasqual's goal 14 minutes into the match gave the visitors a lead they never relinquished in a bad-tempered clash that saw eight players booked.
It was Fiorentina's fifth win of the season and lifted them on to 18 points, one adrift of fourth-placed Lazio.
Genoa remain 16th and still have just two victories to their name this season.
- Sports & Recreation
- Manuel Pasqual