Anderlecht goalkeeper Silvio Proto produced four outstanding saves to frustrate Milan who created more chances despite being outplayed for long periods.
The highlight for Proto came when he somehow blocked a point-blank header from substitute Stephan El Shaarawy just after the hour.
Anderlecht, back in the Champions League after a six-year absence, should have gone ahead shortly before that when Dieudonne Mbokani flicked the ball through to Lucas Biglia who burst into the area but fired over with only keeper Christian Abbiati to beat.
Milan were jeered off by a 27,000 crowd at the 80,000 capacity San Siro after failing to score for the third straight home game this season, having suffered 1-0 defeats by Sampdoria and Atalanta in Serie A.
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