The results left Milan at the top of the group with four points while Anderlecht and Lille remained level with two points each while fourth-place AEK have one point.
The six-time European champions were closer to victory but sublime saves from Tony Sylva denied them the three points.
Brazil playmaker Kaka was instrumental and created several chances but Clarence Seedorf and Alberto Gilardino couldn't convert home.
But Kaka failed to break the deadlock in the 41st minute when he latched on to a deft through pass from Andrea Pirlo, rounded Sylva and sent the ball towards the net.
The Senegalese goalkeeper, though, recovered quickly and blocked the shot brilliantly.
In the 52nd minute, Dutchman Seedorf found the net but his goal was disallowed for offside.
Milan dangerman Filippo Inzaghi was thrown into the fray late in the second period but he hardly had an impact.
Lille almost snatched the win with five minutes remaining on the clock as Yohan Cabaye fired a long-range shot but Milan keeper Dida saved the day for the Italians.
In the Greek capital, Brazilian forward Julio Cesar poked home to give AEK a 1-1 draw with Anderlecht and revive their chances in the group stage.
Nicolas Frutos put the visitors ahead in the 25th minute when he sliced a first-timer home after a superb lob from Mbark Boussoufa.
Cesar leveled the score just three minutes later as his low shot from the edge of the area beat Anderlecht keeper Daniel Zitka.
Egypt captain Ahmed Hassan didn't take part with Anderlecht because of a shoulder injury that ruled him out of the trip.