Eusebio Di Francesco's men had to do things the hard way after falling behind in the seventh minute.
Verona looked lively during the early exchanges and Vangelis Moras nodded them ahead from a corner, the defender scoring his first Serie A goal since May 2009.
Sassuolo eventually drew level in the 50th minute, however, as Nicola Sansone found the net with the outside of his foot from the edge of the box.
The hosts completed the turnaround with 13 minutes to go as Saphir Taider, who had until then done very little, slid in at the back post to secure victory.
The day's late kick-off saw Stefano Pioli return to his former team Chievo with Lazio, who could not find a way past veteran goalkeeper Albano Bizzarri in a 0-0 draw.
Lazio tried to take the initiative as they pushed forward right from the start, with Antonio Candreva and Marco Parolo both going close early on.
Dutch defender Stefan de Vrij almost got the better of Bizzarri with a long-range effort that looked to be dipping just under the crossbar, but the goalkeeper rose to the challenge.
The second half saw Chievo come out of their shells and Mariano Izco went close to breaking the deadlock as he fired into the side-netting.
Bizzarri was the hero on two further occasions in the final 20 minutes, though, the 37-year-old producing a fine save to keep out Stefano Mauri's ferocious half-volley, before saving from De Vrij's late header.
The result sees Chievo move out of the bottom three until Sunday at least, while Lazio failed to move into the top four.
