All the damage was done in a dominant first half for the hosts, with Giovinco opening the scoring early on before setting up Martin Caceres and then Fabio Quagliarella to complete the triumph.
Serie B outfit Avellino showed commendable resolve after the break to keep the final score respectable, but it is Juve who march on to the last eight.
And the home fans were also treated to the sight of Simone Pepe returning to action after an injury-blighted two seasons.
Italy international Giovinco put the hosts ahead with just seven minutes gone, shifting the ball onto his right foot inside the box and curling a superb effort past Giuseppe Di Masi.
Caceres doubled their advantage as Giovinco turned provider with a free-kick nine minutes later, the Uruguay defender grabbing his first of the season.
And Giovinco had a hand in the third before the break, whipping in another set-piece delivery that Quagliarella headed home.
Pepe came off the bench to huge applause from the home fans in an otherwise uneventful second half, which also saw Ouasim Bouy handed his first-team debut.
Juve, who will play the winners of next month's tie between Roma and Sampdoria, moved a step closer to a record-breaking 10th Coppa Italia crown.
