UEFA Champions League: Atletico Madrid 4 Milan 1
Diego Simeone's men, who won the first leg 1-0, triumphed 4-1 at Vincente Calderon in the return game on Tuesday as goals from Diego Costa and Arda Turan sandwiched Kaka's close-range header in the first half.
Raul Garcia and Costa's second added further gloss to the scoreline inside the final 20 minutes.
The hosts were good value for the victory in an entertaining fixture in the Spanish capital and, with just three points separating them from city rivals Real at the top of La Liga, Simeone's side can now continue their assault on the domestic and European front.
Atletico made the perfect start as Costa – who also scored in the first encounter – was once more the thorn in Milan's defence, stretching athletically to meet Koke's sublime cross to score his sixth Champions League goal in five matches.
Former Real Madrid man Kaka threatened a comeback for Clarence Seedorf's men with a close-range header, but Atletico led at the break in fortunate circumstances courtesy of Turan's deflected volley.
The match was wrapped up on 70 minutes when Raul Garcia leapt to head home Gabi's free-kick, before Costa bagged his brace in the closing stages to send Atletico into the quarters for the first time in 17 years.
It took the home side just three minutes to double their first-leg advantage. Koke curled a sublime cross towards the far post and Costa showed great athleticism to divert a side-footed volley past Christian Abbiati.
Milan settled into the encounter after a lacklustre start and were back in the tie on 27 minutes with the equaliser on the night.
The ball was spread wide to Andrea Poli and he stood up a pin-point cross to the back post where Kaka headed home from close range.
The Brazilian then missed a clear chance to put Milan ahead on away goals, as he leapt to meet Adel Taarabt's centre, but succeeded only in heading over from six yards.
That miss proved costly as Turan restored Atletico's lead in fortuitous circumstances five minutes before the break. The Turkey international's volley took a huge deflection off Daniele Bonera before looping over Abbiati and nestling in the bottom corner.
Raul Garcia nearly made it three on the stroke of half-time with an acrobatic free-kick that went just wide.
Atletico started the second half in the same swift fashion that they had started the first and captain Gabi smashed a 20-yard effort against the crossbar on 48 minutes.
Shortly after the hour mark, Costa held up a ball from the byline and Miranda headed straight at Abbiati from eight yards.
The pressure finally told when the tie was put beyond all doubt 20 minutes from time, as Raul Garcia rose high to nod Gabi's free-kick into the bottom corner.
Robinho went close to reducing the deficit when he cracked an effort against the crossbar.
There was time for one last piece of action, however, as Costa fired across goal into the bottom corner in the 85th minute.