Milan looked on course for a well-deserved draw after having the better chances in the match, however Diego Costa struck his fifth goal in four Champions League games in the 83rd minute to win the last 16 first leg clash.
The Serie A side had the better of the first half with excellent opportunities to open the scoring, but they lacked quality in front of goal as Andrea Poli and Kaka both missed good chances, while visiting goalkeeper Thibaut Courtois was in inspired form.
The result gives Atleti a crucial away goal going into the second leg at the Vicente Calderon in three weeks' time.
Diego Simeone's side attacked from the off, though Abbiati was untested and Milan slowly worked their way back into the game with good spells of possession.
The Belgian goalkeeper diverted Kaka’s effort onto the crossbar in the 15th minute, and three minutes later he produced an outstanding stop to tip Poli’s close-range header onto the post.
Clarence Seedorf will have been impressed with his side's performance but they failed to capitalise, Balotelli missing the last chance of the first half as his long-range effort bent wide of goal.
After a quiet opening period, Costa saw an attempted acrobatic volley fly way over the bar and an effort from Raul Garcia went the same way with the midfielder's low effort smothered by Abbiati as chances of a goal looked to be running out.
Adil Rami went close to levelling for Milan with a powerful long-range effort but it flew wide of Courtois' right-hand post and Milan have it all to in Spain on March 11, having won on just one of their last 13 trips to La Liga sides.
