The Italians, who were without an away win so far this season, were gifted two of the goals by some inept Celtic defending.
Kaka opened the scoring after 13 minutes when the home side's defence stood still as Valter Birsa's corner came into the penalty area and the unmarked Brazilian headed home from close range.
Charlie Mulgrew and Derk Boerrigter should have scored before halftime for Celtic, both finishing weakly from inside the Milan area.
But Celtic's best chance fell to defender Virgil van Dijk after 48 minutes when his fierce volley smashed into the body of Milan keeper Christian Abbiati.
A minute later, Milan made it 2-0 from another poorly- defended corner taken by Birsa. Antonio Nocerino was left alone at the back post and he prodded the ball across goal for Cristian Zapata to tap in.
Van Dijk had the ball in the net but was ruled offside then James Forrest shot wide before Milan added a third on the hour.
Mario Balotelli latched onto a long ball by Riccardo Montolivo, out-muscled Efe Ambrose and clipped it past Fraser Forster in the Celtic goal.
The result keeps Milan second in the group table on eight points from five games, two points behind Barcelona who were surprisingly beaten at Ajax, who have seven. Celtic are bottom with three points and go out.
(Reporting By Tony Goodson; Editing by Rex Gowar)
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