Substitute Edin Dzeko continued his fine recent form to level before Lautaro Martinez scored a penalty to complete the second-half turnaround.
Domenico Berardi had put Sassuolo ahead from the spot with his third goal in as many league matches.
Dzeko becomes the first Inter striker to score six goals in his first seven games since Ronaldo in 1997-98.
Sassuolo took the lead after 22 minutes when Berardi fired past Samir Handanovic after Milan Skriniar brought down Jeremie Boga in the box.
It was a tough first half for the visitors, whose only shot on target came when Nicolo Barella forced Andrea Consigli into a smart save, while Handanovic was equal to Berardi’s volley from distance at the other end.
Immediately after coming off the bench as part of a quadruple change just before the hour, Dzeko levelled the scores by heading home Ivan Perisic’s cross at the back post.
The winner arrived 13 minutes from time with Martinez slotting home from the spot after Consigli fouled Dzeko in the box, securing three points and extending Inter’s run of scoring at least twice in a match to 12 successive league games.