The visitors made a strong start to the game and they took the lead in the third minute when Gonzalo Higuain's strike deflected into the path of Marek Hamsik, who fired the ball in from a tight angle.
Higuain threatened again for the visitors moments later with a powerful drive that flew inches wide of the post.
With five minutes of the first half remaining they almost grabbed a second goal, but Gregoire Defrel's powerful shot was saved by the keeper.
In the second half the visitors looked to regain their lead and Dries Mertens flashed a free kick narrowly wide of the far post.
Mertens fired another effort wide, before Jose Callejon dragged a shot inches off target, as Napoli continued to look a threat.
However, with six minutes of the game remaining Sassuolo took the lead, as Diego Falcinelli's cross to the back post was headed in by Sansone.
Napoli tried to salvage a point late on, but they were unable to create any further chances, as their season began on a losing note.