Darko Lazovic met a Nikola Ninkovic cross completely alone on the back post and duly slotted home to give the hosts a lead.
A Mauro Zarate screamer rattled the bar and Federico Bernardeschi should have won a penalty, but Fiorentina never really seemed likely to breach a very physical Genoa defense.
Goals: Lazovic 37’ (ass. Ninkovic)
Cards: Veloso 27’, Ninkovic 59’, Lazovic 77’, Tomovic 19’, Badelj 84’