Barcelona made Champions League history by overturning a two-goal deficit without an away strike to knock out AC Milan and reach the quarter-finals.The Catalans wasted no time and scored in the fifth minute when Lionel Messi expertly curled in from 20 yards.After M’Baye Niang hit the post for the visitors against the run of play, Messi levelled the tie with a low drive.David Villa put Barca ahead with a placed shot from Xavi’s pass and Jordi Alba sealed the win in injury time.The left-back, excellent throughout, showed great endeavour to race up from the back and finish at the far post after he was picked out by substitute Alexis Sanchez’s bouncing cross.For all of Milan’s excellence in the San Siro, that kind of incision had been absent as stand-in Barcelona coach Jordi Roura’s team laboured towards a 2-0 first-leg defeat in which they uncharacteristically registered only one shot on target. Questions had also been raised after that match due to Barca’s successive Spanish Cup and league losses to rivals Real Madrid, as well as a run in which they went 13 games without keeping a clean sheet.But their usual zip returned on the vast Nou Camp pitch from kick-off as they started at a high tempo.This intensity was rewarded immediately as Messi played a neat one-two with Xavi and finished into the top corner with goalkeeper Christian Abbiati rooted to the spot. The goal was the world player of the year’s 52nd of the season, but his first in open play in 10 meetings with Italian sides.In the round of 16 opener, Milan’s tight, disciplined display saw their centre midfielders cover a deep-lying and compact defence which left no gaps for their opponents to run through. Critically, this support was not present on Tuesday as Barca were granted space on the edge of the penalty area.The Italians survived two penalty appeals and a poor Messi header, but the tie’s key moments arrived with just over five minutes of the first half remaining. First, Milan striker Niang struck the woodwork after racing through on goal following a swift counter-attack from a Barca corner.If the France Under-21 international had managed to get an away goal, their opponents would have had to find the back of the net at least three more times to proceed.Instead, Milan’s advantage from the first leg was wiped out moments later as Messi fizzed in an unstoppable shot from 20-yards after Massimo Ambrosini lost possession.Barca continued on the front foot after the interval and went ahead on aggregate for the first time when Villa finished clinically after he was picked out in the box by Xavi. The goal owed much to left-back Kevin Constant’s rash attempt to intercept the pass before it reached the striker.The visitors now knew they had to score to stand any chance of progression and head coach Massimiliano Allegri brought on former Manchester City striker Robinho.This change nearly produced the breakthrough the Serie A side were looking for. Barca youth product and fellow substitute Bojan Krkic put in a low centre that Robinho seemed certain to convert before defender Alba dived across to block the shot.Barca refused to sit back on their lead and a wonderful counter from a Milan free-kick at the death saw the defender further excel at the other end of the pitch when he burst forward to slot past Abbiati and raise the Nou Camp crowd to their feet.