Genoa look set to miss out on a place in the Europa League after Sassuolo built up a 3-1 lead before the interval at the Citta del Tricolore.
The Rossoblu, who need to win and hope that Fiorentina lose at home to Chievo, got off to the worst possible start after Domenico Berardi latched on to Simone Missiroli's through-pass before firing his shot into the top corner of Eugenio Lamanna's net.
Sassuolo almost doubled their lead on 14 minutes when Paolo Cannavaro's shot from the edge of the area was saved by Lamanna.
Moments later, Genoa almost got back on level terms as Maxime Lestienne's strike was kept out by Alberto Pomini.
In the 18th minute, the Green and Blues did double their lead as Berardi turned provider for Simone Zaza and the Italian international duly found the back of the net to give the hosts a healthy advantage.
Just after the half-hour mark, Zaza seemingly put three points beyond the reach of the Genoans when he fired Federico Peluso's cross into the roof of the net.
However, Genoa did pull a goal back before the interval through Leonardo Pavoletti, but with Fiorentina beating Chievo, a fifth-placed finish appears to be unlikely.
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