Juve coach Ciro Ferrara had presided over four defeats in five games but looks safe in his job for now after a victory sealed by two second-half goals from the little-used Alessandro Del Piero, the second a penalty.
The first goal was the main talking point, however, with Brazilian playmaker Diego, a major flop since his big close-season move from Werder Bremen, netted on 24 minutes despite Napoli's Jesus Datolo lying injured on the floor.
Mathieu Flamini earlier spared AC Milan's blushes by netting the winner nine minutes from time in a 2-1 last-16 victory over third tier Novara.
A second-string Milan side allowed Pablo Gonzalez to score just after the break but the hosts prevailed when Flamini's powerful strike set up a meeting with Udinese or Lumezzane, who play on Thursday.
Catania's Gianvinto Plasmati scored twice early on in a 2-1 win at nine-man Genoa and AS Roma beat second division Triestina 3-1 on Tuesday.
