Fiorentina dominated the match, but failed to finish any of their chances, allowing Genoa to emerge with a point.
The Viola kept their side intact, including Giovanni Simeone against his former club, while ex-Viola star Giuseppe Rossi was in the stands of his old hunting ground, as he is still waiting for his Genoa debut.
The last Genoa win away to Fiorentina was 2-1 back in March 1977, followed by nine draws and 11 losses.
Adel Taarabt’s rising solo effort was fingertipped over the crossbar, then Marco Sportiello beat away a Brlek strike. Fiorentina slowly grew into the game, Federico Chiesa’s angled drive flashing just past both the far post and teammate Cristian Biraghi.
Genoa were forced into a substitution before half-time, as Nicolas Spolli went off with a knock to make way for Luca Rosettini.
German Pezzella’s header from a Milan Badelj corner skimmed the far upright, then Simeone ballooned over the bar from a Chiesa pull-back.
Simeone also nodded on to the roof of the net, as Fiorentina dominated the second half. They pushed to the bitter end, but at the 88th minute Luca Rossettini threw himself at Biraghi’s finish like a human shield and the rebound went over the bar.