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 full-backs 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 half-time with a low drive.
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 full-back'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."
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.
