The Catalans were tipped for an early exit from the competition after a 2-0 reverse in Italy, but became the first ever team to recover from that same first-leg scoreline with a display that showcased the best of their awesome attacking quality.
Lionel Messi needed only five minutes to open the scoring in sublime fashion, before putting his side level on aggregate with his second goal shortly before the interval.
David Villa sent Barca into a 3-0 lead minutes into the second-half, and Jordi Alba added the clincher in the last minute of injury time as Milan, despite a late improvement, could have little complaints about the result after they were simply overrun.
Xavi recovered from a hamstring injury in time to start in the hosts’ midfield, while Villa and Pedro were the ones chosen to line up alongside Messi in attack.
Meanwhile, with Giampaolo Pazzini injured and Mario Balotelli ineligible, the Rossoneri lined up with M’Baye Niang, Stephan El Shaarawy and Kevin-Prince Boateng up front.
Barca were dominant right from the first whistle, and were rewarded with the opening goal on five minutes, when Messi linked beautifully with Xavi for a one-two, and curled an equally sublime effort in from the edge of the box.
The first half was shaping up to be a one-sided affair, with Milan hanging on for dear life against wave after wave of Barca attacks.
Ignazio Abate avoided conceding a penalty for a push on Pedro, before Christian Abbiati did excellently to push a splendid half-volley from Andres Iniesta onto the crossbar – with Messi nodding the rebound into the side netting.
Abbiati repeated the trick by tipping a Xavi piledriver around the post, but as the first half progressed, the home side’s chances dried up as Milan began to compose themselves at the back.
And with half time seven minutes away, the visitors nearly struck the killer blow at the other end of the pitch.
A terrible header from Javier Mascherano let in Niang, who had time to pick his spot, but struck the base of the post, leaving the visiting fans grimacing in agony.
And Niang’s miss would become far more costly two minutes later, when Iniesta found Messi lurking, who drilled precisely into the corner from just outside the area.
The Argentine was at it again immediately after the restart, pouncing on a Kevin Constant giveaway, but after storming into to box, he failed to seriously trouble Abbiati with his finish.
But with 55 minutes on the clock, the Catalans would strike again to finally move ahead in the tie. Xavi’s fantastic pass picked out Villa on the right, who shifted the ball onto his left foot and bent a fine finish into the far corner.
Milan now had to score to progress, and Allegri responded by throwing on Robinho and Sulley Muntari for Niang and Massimo Ambrosini.
The Rossoneri improved in the latter stages of the second half, with both Gerard Pique and Alba forced into last-ditch challenges inside the area, though they were somewhat fortunate to see an Alexis Sanchez goal disallowed for offside.
But they still were woefully inadequate up front, and with the seconds ticking away, Alba stole in down the left to latch onto Sanchez's pass and clip a finish over Abbiati to wrap up the victory.