Barcelona pulled off a remarkable Champions League comeback when Lionel Messi scored twice in a thrilling 4-0 home win over AC Milan on Tuesday that sent the Spaniards through to the last eight 4-2 on aggregate Trailing from last month's last 16, first leg at the San Siro, Barca were ahead in the fifth minute at a raucous Nou Camp thanks to Messi's brilliant curling effort and the World Player of the Year levelled the tie on aggregate five minutes before halftime with a powerful low drive. Barca ruthlessly dominated the Italians, who struggled to get the ball out of their own half for long periods, and David Villa struck a third for the hosts 10 minutes after the break before Jordi Alba killed off Milan with a breakaway goal in the second minute of added time. Barca are 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. The early goal helped us a lot, but it was something we looked for from the first minute," Villa told Spanish television. "We believed we could do it from the first minute, in fact from the final whistle of the last game. "We are delighted for the fans. We always believed we could do it. For them, and with them, we have done it." Roared on by close to 90,000 supporters inside their giant arena, fired-up Barca harried and hassled Milan from the start. EARLY GOAL 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 intensity 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. Barcelona 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. 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 Messi who smashed a low drive past Abbiati from just outside the penalty area. 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 struck 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 which eased the tension among the home fans and killed off Milan's hopes. The Serie A side had pressed forward looking for the goal that would have sent them through but Barca held out relatively comfortably to keep alive their dream of a third European crown in five years. (For more sports news and updates, follow Ahram Online Sports on Twitter at @AO Sports and on Facebook at AhramOnlineSports)