Costa double propels Atletico into the last eight
Atletico Madrid's midfielder Raul Garcia (L) celebrates with Brazilian-born forward Diego da Silva Costa after scoring at the Vicente Calderon stadium in Madrid on March 11, 2014 - by Pierre-Philippe Marcou
Diego Costa struck the winner in the first leg three weeks ago and it took him just three minutes to double Atletico's advantage as he acrobatically turned home Koke's cross.
Milan were given hope when Kaka headed home Andrea Poli's cross on 27 minutes, but Arda Turan restored Atletico's lead on the night before half-time when his volley from the edge of the box deflected past Christian Abbiati.
Raul Garcia's header made it 3-1 before Costa rounded off a fine individual display with his seventh Champions League goal of the campaign six minutes from time.
Milan boss Clarence Seedorf had insisted pre-match that the tie was still open despite losing the first leg at home, but it looked as if the Italian's hopes had been killed off within minutes as Gabi robbed the ball from on the right, fed Koke and his cross was hooked home on the volley by Costa for his 28th goal of the season.
The hosts were dealt a blow moments later, though, as Garcia was shown a yellow card that will keep him out of the first leg of their quarter-final tie.
After an early burst from Atletico, Milan were enjoying plenty of possession midway through the half, but didn't look threatening until a lovely move opened up the Spanish side just before the half hour.
Mario Balotelli sprayed the ball wide to Poli and his cross was headed home at the back post by Kaka, though, it took a deflection off Miranda.
The Milan captain then had a great chance to put his side ahead in the tie on away goal when he nodded Adel Taarabt's inviting cross just over.
Just four minutes later, the seven-time European champions were left to rue that miss as Garcia chested down for Arda on the edge of the box and his shot cannoned off Adil Rami and past the helpless Abbiati.
Garcia then came within inches of sealing the tie with a spectacular overhead kick from Juanfran's cross that flew just past the far post
Atletico had another great chance to put the tie to bed within three minutes of the restart for the second-half as a rapid counter-attack from a Milan corner saw Costa tee up Gabi and his fierce strike came back off the outside of the post.
Just as in the first-half Milan grew into the game as the half progressed and Thibaut Courtois had to dive low to his left to parry substitute Robinho's low drive across the box.
Diego Simeone's men did finally get the two-goal cushion on the night they craved when Garcia rose highest to power home Gabi's free-kick 20 minutes from time.
Robinho nearly responded immediately as he blasted Kaka's neat through ball onto the bar with Courtois beaten.
However, it was Atletico who were able to round off their first victory in a knockout tie of Europe's premier club competition since 1978 when Costa arrowed in his second of the night off the far post.