The second-tier side put up a good fight in the first period at Stadio Citta del Tricolore and went into the break level, but the Serie A club's quality eventually shone through.
Claudio Coralli's 33rd-minute equaliser brought the visitors back into the contest after Simone Zaza had opened the scoring from Domenico Berardi's corner early on, but the second half was a different story.
The highly rated Berardi was influential again as Sassuolo took the lead soon after the break.
Former Udinese striker Antonio Floro Flores put the match beyond any doubt in second-half stoppage time, ensuring their passage to the fourth round.
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