Substitute Dybala put Roma ahead in the 64th minute, with the Argentine sending a powerful shot from a tight angle inside the far post after replacing midfielder Lorenzo Pellegrini at halftime.
See stats from the match at Flashscore
Earlier on Thursday, Fiorentina advanced to the quarter-finals with a 1-0 win over Sampdoria.
Serie A leaders Napoli host bottom-placed Cremonese on Tuesday. Atalanta, Lazio and Juventus play their last-16 ties next Thursday.