Torino beat Pescara 4-1 to progress in the Coppa Italia, while Carpi needed extra time to see off Livorno 2-0.
Serie A outfits Empoli and Bologna both endured shock exits from the competition this weekend, but the Granata gave a confident performance.
The visitors took a shock lead after 17 minutes thanks to an own goal by Toro goalkeeper Salvador Ichazo.
However, new signing Daniele Baselli drew the home side level ten minutes later after a great assist from Fabio Quagliarella.
Fellow debutant Afriyie Acquah then put Torino in front on the 33rd minute, before second half goals from Maxi Lopez and Josef Martinez completed the rout.
Meanwhile, nothing could separate Carpi and Livorno over 90 minutes, with a double from Ryder Matos in extra time eventually seeing the Serie A debutants through safely.
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