Marco Parolo's early goal was enough for the Gialloblu, who moved ahead of Hellas Verona into the final Europa League place.
Sassuolo were dominated throughout and their afternoon got even worse in the second half when substitute Domenico Berardi was sent off only a minute after his introduction, damaging any hope of an already unlikely comeback.
The goal came inside two minutes as Jonathan Biabiany's cross from the right was met by Parolo, who sidefooted inside the near post.
Alessandro Lucarelli was denied a second in the 13th minute, adjudged to be just offside when he converted Antonio Cassano's cross.
Cassano curled inches beyond the far post and Biabiany teed up Amauri to fire just over as the visitors sought to kill the game off early.
A rare Sassuolo attack saw them win a free-kick on the edge of the box, but Simone Zaza's wasteful shot over summed up a day of struggle.
Amauri missed from close range late in the first half and Biabiany was denied by goalkeeper Gianluca Pegolo early in the second 45 minutes.
Marco Marchionni was next to threaten, shooting just wide from 20 yards, while Pegolo saved from point-blank range when Cassano should have left him with no chance.
If such a series of escapes led Sassuolo to believe they could steal a point, their hopes were undermined by Berardi's recklessness.
The forward replaced midfielder Raffaele Pucino in the 71st minute but scarcely more than 60 seconds later he foolishly threw an elbow at Cristian Molinaro and quickly left the arena once more.
Lucarelli's header from Mattia Cassani's corner was cleared off the line by Lorenzo Ariaudo and Parma squandered another good chance late on, Ezequiel Schelotto shooting wide when Pegolo parried Parolo's shot straight to him, but it mattered little.