Barcelona 4 Milan 0 match report: Lionel Messi the magician conjures up Barça's stunning Champions League escape act

Such is their complete domination of almost all La Liga matches the less-committed Barcelona supporters can be in the car park before the final whistle. Tonight as the board was held up for added time, no-one had moved from their seat.

When Jordi Alba swept in the fourth they celebrated a job well done; and such was the emotion, the home fans stayed beyond the final whistle to savor their side's passing into the last eight – the first team to come back from a 2-0 defeat in the first leg in the Champions League era.

There were many heroes but Barça's brilliant No 10 was the catalyst for this famous win. In Rome they deliberate over the identity of the new pope. In Barcelona god is still Lionel Messi. With minimum fuss and little concern for the defenders who surrounded him, he twice thrashed first-half shots past Milan keeper Christian Abbiati to leave his side needing just a third.

"Just" can be a big word in the Champions League and Milan always threatened on the break. But David Villa delivered and then as Milan laid siege on an exhausted Barcelona defence, Alba got the fourth to put the result beyond doubt.

It was a performance that would have had even Jose Mourinho doffing his cap in Madrid. He must have thought he had seen the back of Messi and Co after their first-leg defeat in San Siro – now the draw could throw Barça and Real Madrid together in the quarter-finals.

Mourinho will also have noted that this was the Barcelona of old; the team who have reached two of the last four Champions League finals; the team that are 13 points clear of the field in Spain.

They played so high up the pitch keeper Victor Valdes was often left alone in his own half. Villa went through the middle, occupying Milan's central defenders and leaving Messi to float across the line of the penalty area linking with Andres Iniesta and Xavi – the old Bermuda triangle in which so many sides have found themselves lost before.

Milan will have expected the home side to attack relentlessly from the start but the contrast in intensity from the first leg was still stark. At San Siro Messi had not mustered a shot on target, here he had his first effort in the fifth minute and it hit the back of Abbiati's net.

Xavi found him just inside the Milan penalty area and despite four white-shirted Milan defenders surrounding him the Argentine flashed a shot into the top corner. Gerard Pique had said before the game that any Barcelona supporters who did not believe the comeback was possible should give their ticket to someone else. If there were any doubters in the stadium at kick-off they were all believers now.

Barça then had a good penalty claim turned down when Pedro ran on to a long Xavi's long pass and appeared to be bundled over by Ignazio Abate. Abbiati pushed Iniesta's shot on to the bar and Messi headed the rebound into the side-netting.

As their early energy waned Milan had chances. Massimo Ambrosini robbed Messi and sent Stephan El Shaarawy clear but the Milan forward shot weakly at Valdes. Then came the moment that could have swung the tie irreversibly in the visitors' favour.

M'Baye Niang dispossessed Javier Mascherano and honed in on Victor Valdes' goal. He beat the keeper but his shot bounced off the base of the post. Barça grabbed the initiative back and made Milan pay for the miss.

This time it was Iniesta who loaded the bullet, once again it was Messi who pulled the trigger – cutting inside from the right five minutes before half-time and beating Abbiati with a low shot that made it 53 goals this season for him, and more importantly levelled the tie.

Messi started the second half almost as well as he had finished the first with the first shot on goal saved by Abbiati. Mathieu Flamini then clattered into Xavi, both he and Kevin-Prince Boateng had been booked in the first half. Flamini would now miss the next round but it was becoming increasingly clear that so would his team-mates.

Mascherano brilliantly won possession, Xavi then found Villa in space to the right of the Milan penalty area and he flashed a shot into the far corner. All the rage of a player scandalously under-used all season came to the surface in wild celebration – Barça were ahead on aggregate for the first time.

Milan were still just one goal from going through on away goals though and when Pique pirouetted precariously in his own half with substitute Bojan Krkic close by the Nou Camp's collective heart was in its mouth. Then in added time Messi fed Alexis Sanchez and Alba raced onto his cross to calmly beat Abbiati.

"We believed we could do it from the first minute, in fact from the final whistle of the last game," said Villa. "We started really fired up, as you have seen. The early goal helped us a lot, but it was something we looked for from the first minute." Alba added: "We have seen the return of the old Barcelona tonight."

The players had promised missing coach Tito Vilanova a 3-0 scoreline, they had gone one better and when he comes back at the start of next month his team will still be in the Champions League.

Man of the match Messi.

Match rating 9/10.

Referee V Kassai (Hun).

Attendance 96,000.