With the likes of Stephan El Shaarawy and Antonio Nocerino rested, the Rossoneri were made to wait to flex their muscles, all three goals coming in the second half.
Mario Yepes opened the scoring six minutes after the break before M'Baye Niang doubled Milan's advantage with 11 minutes remaining.
Giampaolo Pazzini completed the scoring with a third on 81 minutes to seal Massimiliano Allegri's side's place in the last eight, where they will face Juventus.
The Old Lady beat lowly Cagliari 1-0 on Wednesday to ensure their progress.
