The Spanish outfit entered the match as underdogs having trailed 2-0 from the first leg, but they had the lead on the night inside five minutes when Messi struck from the edge of the box. The Argentine added his second to level the tie at 2-2 moments before the interval.
Milan improved in the early stages of the second period, but a goal from David Villa in the 55th minute sent Barcelona into a 3-0 lead on the night.
The Italian side pushed for the goal that would have taken them into the next round in the latter stages, but they were stung on the counter as Jordi Alba made it 4-0 on the night in stoppage time.
Here, Sports Mole dissects the 90 minutes of action between the two European rivals.
On target: 7
On target: 2
Was the result fair?
It is difficult to argue that Barcelona did not deserve a spot in the quarter-finals of the competition. They had plenty to do after losing 2-0 in Milan, but they started the match with such a tempo and deservedly led inside five minutes. Milan had chances of their own, but the Spanish outfit were never too concerned as they eased into the final eight 4-2 on aggregate.
The Catalan outfit needed to respond this evening following a host of poor performances in recent weeks, which they certainly did. This was the Barcelona of old as they utterly passed Milan into submission. The early goal certainly helped ease the nerves, but they were the better side all evening. Aside from their attacking play, the clean sheet would also have pleased them this evening.
AC Milan's performance
In truth, Milan did not do a lot wrong this evening. It is hard to justify that statement when they have been beaten 4-0, but they came up against the best team in the world in full flow. They were guilty of poor passing in the final third, especially in the opening half, but there was never enough room to really create an opening. They will take positives from the match with bright displays from their younger generation.
Sports Mole's man of the match
Jordi Alba: Messi might have scored twice this evening, but Alba was just sensational. Having joined from Valencia in the summer of 2012, he has emerged into the best left-back in world football. He made a stunning block on Robinho at 3-0 before adding a goal of his own in the latter stages. Wonderful all-round display from the Spanish international.
Biggest gaffe of the match
There are always defining moments in Champions League matches. Mbaye Niang had a wonderful chance to level the scores at 1-1 when he advanced on goal in the first period, but he struck the post and moments later Messi scored his second. That was ultimately the turning moment in the match.
Viktor Kassai had a very productive 90 minutes of action this evening. The Hungarian rightly turned down two penalty appeals for Barcelona in the first period, while he was not prepared to issue a card for every challenge. Behind every great match there is a great referee.
Barcelona: The Spanish outfit will attempt to extend their lead at the top of the La Liga table when they welcome Rayo Vallecano on Sunday.
AC Milan: Milan also return to domestic action this weekend with a home match against Palermo.