The Rossoneri, who had been struggling for form prior, were able to brush aside the challenge of the Scottish champions who have now crashed out of both European competitions after Ajax upset Barcelona in Amsterdam.
A revitalized Kaka opened the scoring for Milan in the 13th minute when he found himself unmarked in the six-yard box to head home Valter Birsa's corner past a hapless Fraser Forster.
Milan made the home side pay when they doubled their lead in the 49th minute courtesy of Cristian Zapata who tapped home substitute Antonio Nocerino's pass at the back post.
Maximiliano Allegri's side host the Dutch giants on December 11 with a draw enough to see them through while Celtic head to the Nou Camp in the hope of improving their current record of one win and four losses.
2013/14 UEFA Champions League - Group H scores
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