Diego Costa's 83rd-minute goal separated the two sides after the Rossoneri were unlucky not to have taken the lead in the opening 45 minutes.
Kaka fired into the crossbar in the 14th minute before Andrea Poli's header less than five minutes later was knocked into the upright by Los Rojiblancos keeper Thibaut Courtois who had also managed to tip Kaka's effort on.
Milan again had opportunities in the second half with Kaka firing wide and Michael Essien missing the target with a header and their wastefulness in front of goal proved to be costly.
Gabi's corner seven minutes from time was inadvertently flicked on by Milan defender Ignazio Abate at the front post only for Costa to backtrack under the looping ball to head home past Abbiati for his fifth goal of the competition.
Clarence Seedorf will need to get his Rossoneri outfit up to scratch for the return leg at the Estadio Vicente Calderon on March 11 as Diego Simeone's Atleti have lost just once at home in their past 22 outings.
2013/14 UEFA Champions League - Round of 16 first leg
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