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.

"It is a great moment and we have to enjoy it," said Atletico boss Diego Simeone, who was playing for the club the last time they reached the quarter-finals.

"We know whoever we face next will be an extremely difficult opponent so now we have to rest and enjoy the fruits of our work."

Costa's two goals took his tally for the season to 29 and he hailed the impact made by the Atletico fans.

"The fans were great and they always support not only me, but everyone," Costa told Television Espanola.

"We have to congratulate ourselves for the game we played.

"Now we are in the quarter-finals you cannot choose who you face because they are all so good. We have to enjoy it, but also think about La Liga at the weekend."

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 Koke's cross was hooked home on the volley by Costa.

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.

And Seedorf admitted that was the goal that sapped his side's belief.

"For a game and a half we saw a very good AC Milan side," he said.

"The team responded with courage from a great goal by Costa until their second goal, that was a very tough blow to overcome.

"The players tried to react, but they weren't able to."

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.

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.