A fired-up Lionel Messi answered his critics by inspiring Barcelona to a sensational Champions League comeback against AC Milan on Tuesday with two goals in a 4-0 home win to help them reach the quarter-finals.

A rampant Barca, all-but written off after a surprise 2-0 reverse at Milan's San Siro stadium in last month's last 16, first leg, came storming back at the seven-times European Cup winners to progress 4-2 on aggregate after a memorable night.

They looked to Messi to spark a fightback and the four-times World Player of the Year did not disappoint with a scintillating display backed up by midfield trio Xavi, Andres Iniesta and Sergio Busquets and fullbacks Jordi Alba and Daniel Alves.

Barca were ahead at the Nou Camp in the fifth minute through Messi's brilliant curling effort and the Argentina forward, who has suffered rare criticism in recent weeks, levelled the tie on aggregate five minutes before halftime with a low drive.

Barcelona ruthlessly dominated, with Milan struggling to get the ball out of their own half for long periods, and David Villa struck a third 10 minutes after the break before Jordi Alba netted a breakaway goal in the second minute of added time.

Before Alba's effort finally killed the tie, Milan had pressed forward looking for the goal that could have sent them through and there was a palpable release of tension in the giant arena when the Spain fullback's shot hit the back of the net before the celebrations began in earnest.

Barca's win makes them the first team in the Champions League to ever overturn a two-goal first leg deficit without the benefit of an away goal while only four sides had successfully fought back from a deficit of more than one goal.

"We started really fired up, as you have seen," Villa told Spanish television.

"The early goal helped us a lot, but it was something we looked for from the first minute," added the Spain forward, who has struggled for form since returning from a broken leg sustained at the end of 2011.

"We believed we could do it from the first minute, in fact from the final whistle of the last game," he said.

"We are delighted for the fans. We always believed we could do it. For them, and with them, we have done it."

EARLY GOAL

Roared on by close to 90,000 supporters, Barca harried and hassled Milan from the start.

The early goal they desperately needed arrived when Messi exchanged passes with Xavi on the edge of the Milan area and curled a brilliant shot into the top corner that left goalkeeper Christian Abbiati rooted to the spot.

Milan were under increasing pressure and Abbiati palmed an Iniesta volley against the crossbar eight minutes later before a long-range Xavi strike flew narrowly wide.

Barca's early intensity inevitably dipped as the half wore on and Milan came within a whisker of snatching the goal that would have meant the hosts needed to score at least three times to go through.

Barca centre back Javier Mascherano misjudged a header and Milan striker M'Baye Niang raced clear but his low shot crashed back off the post with home keeper Victor Valdes beaten. It would prove to be the turning point in the tie.

Moments later Barca doubled their lead on the night and drew level at 2-2 on aggregate. Andres Iniesta won the ball in midfield and fed the irrepressible Messi who smashed a low drive past Abbiati from just outside the penalty area.

It was his 58th Champions League goal, putting him two clear of former Manchester United and Real Madrid striker Ruud van Nistelrooy in second place on the scoring chart behind Raul, another former Real forward, who leads on 71.

Barca continued to dominate in the second half and Villa justified his inclusion in the starting lineup when Xavi sent him clear on the right and he set himself before striking a perfect left-foot shot high into the corner.

The Spain forward made way for Alexis Sanchez 15 minutes from time and it was the Chilean who set up Alba to fire home Barca's fourth.

OLD BARCELONA

"We have seen the return of the old Barcelona and now we need to continue in the same vein," Alba said in an interview with Spanish television.

"With what remains of the season we need to keep playing with the same enthusiasm, intensity and hunger we showed today," he added.

"All of Barcelona came together today for this historic comeback so we are delighted. Today we were on form, but we weren't in Milan. We need to learn from this."

Barca can now look ahead to the last eight after keeping alive their dream of a third European crown in five years and will find out their opponents in Friday's draw.

Milan, third in Serie A, return home to focus on qualifying for the Champions League again next season after coming remarkably close to upsetting the pre-tournament favourites.

"It has been an extraordinary match from Barcelona," Milan coach Massimiliano Allegri told Sky Italia.

"But this is not the disastrous result it will maybe be depicted as but a chance to grow," he added.

"To lose and go out after the first leg we produced at home upsets all of us but the lads shouldn't beat themselves up."