Sassuolo became the latest Serie A victims of a Coppa Italia shock as they were beaten 1-0 at home by Cagliari.
The second-tier visitors, relegated from the top flight last season, booked a last-16 meeting with Inter courtesy of Marco Sau's goal.
Sassuolo have been in fine form in the league, climbing to sixth and only one point behind champions Juventus, but Eusebio Di Francesco's side were well below par on Thursday.
They join fellow top-division outfits Bologna, Chievo, Empoli and Palermo in making early exits from the competition.
Elsewhere, Carpi avoided any such slip-up as they defeated Vicenza 2-1, who ended the match with 10 men.
All the action happened after the break, with Matos' header putting hosts Carpi ahead before Mario Sampirisi saw red for the underdogs, conceding a penalty that was converted by Marco Borriello.
Leonardo Gatto's consolation mattered little, with Carpi now set to meet Fiorentina.
