Serie A side Empoli crashed out of the Coppa Italia in their first game in this year's competition, losing 1-0 to Vicenza on Saturday.
Leonardo Gatto's 53rd-minute goal was the difference as second-tier Vicenza advanced to the fourth round.
Frosinone, newly promoted to Serie A this season, were also eliminated, losing to Spezia 6-5 on penalties after neither side could find a breakthrough in 120 minutes.
Palermo advanced with a 2-1 win over Serie B's Avellino.
Luca Rigoni opened the scoring for Palermo in the second half. Marcello Trotta equalised on the hour mark but Robin Quaison put the top-tier club ahead for good two minutes later.
Diego Falcinelli and Antonio Floro Flores scored to lift Sassuolo to a 2-0 win over Modena.
Hellas Verona erased an early deficit to defeat Lega Pro side Foggia 3-1.
After Giuseppe Loiacono's opener, Emil Hallfredsson quickly equalised, and second-half goals from Luca Toni and Bosko Jankovic put Verona through.
Atalanta cruised past Cittadella 3-0 on goals from Marten de Roon, Maxi Moralez and Mauricio Pinilla.
In games between lower-division sides, Cagliari won 4-2 on penalties to see off Trapani after a 1-1 game, and Alessandria defeated Juve Stabia 1-0.