Roberto Pereyra, Paul Pogba, Alvaro Morata and Kingsley Coman also got on the scoresheet as the hosts made light of eight changes at the Juventus Stadium.
Verona, who face a difficult league clash against the same opponents on Sunday, claimed a second-half consolation through Nene.
Giovinco opened the scoring after just five minutes as he smashed home a free-kick from 25 yards and narrowly missed with another soon after.
Pereyra did double the lead with a deft finish after 21 minutes – his first goal for the club – before Giovinco tapped in his second on the stroke of half-time.
Pogba extended the lead further eight minutes into the second period after some nifty footwork in the box before Nene produced a reply before the hour.
Morata converted from the penalty spot after Giovinco was fouled and teenage substitute Coman wrapped up the scoring with a spectacular sixth, crashing in a shot off the bar, five minutes from time.