Diego Simeone's Los Rojiblancos took a one-goal lead into the return bout at the Vicente Calderon after Diego Costa's late winner at the San Siro last month and within minutes had doubled their advantage.
Milan would love to see the back of Costa now after the Brazil-born Spain international produced a volley with a great degree of difficulty to steer Koke's third-minute stand-up cross past Christian Abbiati.
That early goal did kick Clarence Seedorf's side into gear and on 27 minutes, Kaka arrived perfectly at the back post to finish Andrea Poli's rightwing cross with a rare header that deflected past Thibaut Courtois from inside the six-yard box.
But just as the Rossoneri thought they were back in at 2-1 overall, Atleti powered ahead again on the night when Arda Turan ripped a speculative effort from just outside the area which took a wicked deflection off former Valencia man Adil Rami and floated over Abbiati with just five minutes remaining in the half.
Milan needed a huge second-half effort to get themselves back in the game but all their hopes were crushed just under 20 minutes from time when Raul Garcia rose to meet Gabi's free-kick and head home for a third of the night.
But the Spaniards were not done there as Costa wrapped it up in the 85th minute with his seventh Champions League strike of the campaign and 28th in all competitions this season when he fired beyond Abbiati from an angle.
Atletico are now into the quarter-finals for the first time in 17 years as they took their recent European record to seven wins in eight matches and four Champions League home wins on the trot.
2013/14 UEFA Champions League - Round of 16 second leg
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