Gennaro Gattuso’s fourth-placed side are now unbeaten in their last eight league matches and the latest victory moved them within a point of third-placed Inter Milan.
Polish striker Krysztof Piatek, who has made an explosive start to his time at the club, put Milan in front at the San Siro with his seventh goal in five games since joining the from Genoa in January.
Piatek, who had been too isolated in the first half, reacted well four minutes after the interval to slide the ball home after a neat passing move from the Rossoneri.
Two minutes later Franck Kessie doubled the lead for Milan with a deft chip after a fine run and through ball from Spanish winger Samu Castillejo.
The lively Castillejo added the third, meeting a low cross from Andrea Conti with an angled side-foot finish.
It could have been four for Milan when Fabio Borini had the ball in the net but the effort was disallowed for offside following a VAR review.
Serie A leaders Juventus visit Bologna on Sunday while second-placed Napoli travel to Parma.
Inter will hope to regain their four-point advantage over Milan when they play at Fiorentina on Sunday.
(Reporting by Simon Evans, editing by Ed Osmond)
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