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With half time approaching, Sassuolo thought that they had a great chance to equalise when referee Nicola Rizzoli appeared to award them a penalty.
However, he then reversed his decision to the anger of the home fans.
Roma looked comfortable in the second half and put the result beyond doubt when Michel Bastos scored with virtually the last kick of the game.
The Giallorossi move nine points clear of third-placed Napoli but are still 11 shy of leaders Juventus.
Sassuolo, meanwhile, remain five points adrift of safety in the bottom three.