When Alberto Aquilani fired La Viola ahead midway through the second half, Vincenzo Montella's men were four points clear of European rivals Inter Milan going into the international break.
But the second half was a frenetic affair and Juan Cuadrado had to restore Fiorentina's lead after Daniele Portanova levelled on the hour mark.
There was a brief period of deadlock following Luca Antonelli's unopposed equaliser but Andrea Bertolacci's dismissal gave Fiorentina time and space to force Cassani into a critical error with time running out.
The result allowed Fiorentina to stay in touch with third-placed AC Milan and out of the reach of Inter, whose game at Sampdoria was postponed due to heavy rain.
It was 17th-placed Genoa who started more brightly, though, with Bertolacci blasting over the bar following a mistake from David Pizarro.
The hosts rallied and Adem Ljajic only just missed the target when springing the offside trap to reach a through-ball from Stevan Jovetic.
Ljajic was heavily involved when Aquilani opened the scoring in the 33rd minute, the former Liverpool man tapping home his team-mate's pullback with ease after muscling past Andreas Granqvist.
Fiorentina rode out the half but Genoa were revitalised after the break and home goalkeeper Emiliano Viviano did well to punch a Juan Manuel Vargas free-kick out from underneath his crossbar.
But the Rossoblu did find their equaliser from the resulting corner in the 59th minute as Portanova beat Viviano with a free header from six yards.
Viviano had perhaps been a little unlucky but his counterpart could have no excuses when shipping Fiorentina's second three minutes later.
Manuel Pasqual's cross to Cuadrado appeared errant and largely harmless but Alexandros Tzorvas' terrible handling allowed the Colombian winger to convert an easy header.
The game opened up once again and, after Cristobal Jorquera had blasted past a post, Genoa drew level in the 69th minute. Bosko Jankovic showed perfect control to knock down a cross and slide the ball over to Antonelli, who turned it in from close range.
With each side matching the other blow for blow it was difficult to predict who would come out on top but Fiorentina's task was made much easier in the 76th minute.
Having received his first yellow card just before the break, a second booking for Bertolacci saw Genoa reduced to 10 men and the hosts piling forward in search of a winner.
That goal would not arrive through Gonzalo Rodriguez, who connected well with an inswinging corner, but the ball did ricochet off Cassani and into the back of the net.