An early Domenico Berardi strike and a brace from Italy international Simone Zaza helped the Green and Blacks to victory at the Citta del Tricolore against the Rossoblu, who finished the game with 10 men after Armando Izzo's late sending-off.
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Genoa's push to overhaul Fiorentina in fifth place suffered an immediate setback as a through-ball from Simone Missiroli allowed Berardi to give Sassuolo the lead inside three minutes.
However, the Genoa keeper could do nothing when Berardi's cross found Zaza, who turned the ball into the back of the net to double Sassuolo's advantage.
On 32 minutes, the Rossoblu's hopes of a top-five place were in tatters as Zaza scored his second of the match after latching on to a Federico Peluso cross.
A close-range goal from Leonardo Pavoletti saw Genoa pull a goal back and give themselves hope of a stirring fightback.
Sassuolo were awarded a penalty on 68 minutes for Izzo's foul on Peluso, but Zaza was denied a hat-trick when Lamanna saved his spot kick.
Genoa's hopes of launching a fightback took a blow when Izzo was sent off moments later, and Sassuolo held on for a victory that sees them finish 12th in the Serie A table.