The win completes a historic comeback that took his side into the quarterfinals of the Champions League on Tuesday.
Barcelona won 4-2 on aggregate after a spectacular second leg in the last 16, entering the record books as the first team to turn around a 2-0 first-leg away loss in the competition.
Barcelona imposed its attack from the start and Messi finished off a team move just five minutes in to give the hosts a huge boost of confidence.
Messi struck with another left-footed strike in the 40th to level the contest over two legs.
And Barcelona's relentless pressure paid off in the 55th when David Villa netted the decisive goal before Jordi Alba added a fourth in stoppage time.
Barcelona joins Galatasaray in the last eight after the Turkish side beat Schalke 3-2 on the night and 4-3 on aggregate.
Style
Against the odds, Barcelona reached the quarterfinals for a sixth straight season and kept alive its bid for a fourth title in eight years.
And Messi made sure they did so in style.
Messi moved past Ruud van Nistelrooy (56) into sole possession of second place on the Champions League career scoring list with 58 goals at just 25 years old, trailing only Raul Gonzalez's 71.
The sluggish and tired Barcelona from the loss at San Siro three weeks ago and defeats to fierce rival Real Madrid was nowhere to be seen at Camp Nou on Tuesday night.
Barcelona put on yet another breathtaking display, the kind that has led it to 14 titles since 2008 and earned its place among the best teams to have played the game.
It went forward with orchestrated precision both in its passing and shot taking, and defended tenaciously, asphyxiating Milan's attack before it could ever get started.
New faces
Barcelona assistant coach Jordi Roura, who has been in charge since January with manager Tito Vilanova in New York treating a throat tumor, made two changes to the starting 11 that lost in Italy three weeks ago.
Villa replaced Cesc Fabregas, giving the team the same front three of Villa, Messi and Pedro Rodriguez from the 2011 final win over Manchester United.
Villa's inclusion moved Andres Iniesta back into midfield alongside Xavi Hernandez, who returned from a leg injury he picked up at the San Siro.
Javier Mascherano replaced captain Carles Puyol in defense.
Milan coach Massimiliano Allegri also opted for two new faces, with Mathieu Flamini and M'Baye Niang coming in for the injured forward Giampaolo Pazzini, while first-leg goalscorer Sulley Muntari was left on the bench.
Kevin-Prince Boateng, who also scored in the first game, and defender Philippe Mexes both started despite injury worries.
Early strike
Messi already pulled one goal back for Barcelona before Milan was even able to get the ball, much less string two passes together.
Barcelona struck early through an exquisite flurry of one-touch passes that eluded them in recent matches.
Messi received Sergio Busquets' pass outside the area, laid the ball off for Xavi, who slid it back for Messi to unleashed an unstoppable left-footed curling strike that left goalkeeper Christian Abbiati helpless as it ripped into the top left corner of his net.
Barcelona kept pouring forward and Iniesta went close in the 13th, drawing a save from Abbiati, who pushed his strike onto the crossbar before breathing a sigh of relief when Messi headed the rebound into the side netting.
With Milan rattled and Barcelona's passing attack fully flowing, Abbiati was called on again in the 17th to graze Xavi's long strike just enough to send it by his far upright.
Except for Stephan El Shaarawy's shot in the 34th off the break, Milan's lack of ball control allowed Barcelona to dominate possession and keep most of the action in the final third of the pitch.
Even so, an error by Mascherano gave Milan the perfect chance to score in the 38th when he headed a high ball back toward his own goal.
Aggressive defending
Niang raced onto the ball and shot last the outrushing Valdes, only to see his strike hit the left post.
And just two minutes later Messi leveled the series when Iniesta stole the ball in Milan's half and passed to his teammate on the edge of the area.
Messi quickly put the ball on his favorite left boot and rifled a shot under the legs of Mexes and the outstretched Abbiati to send the home crowd into ecstatic chants of his name.
Barcelona turned the tie in its favour for good thanks to its aggressive defending.
Mascherano surged forward to intercept a pass inside Milan's territory, with the ball passing through Iniesta to Xavi, who fed a through pass by the diving Kevin Constant for Villa to size up Abbiati and swerve a strike into the far side of the net.
Milan still got once last-gasp opportunity from substitute Robinho, but Jordi Alba hustled back to block his close-range attempt in the 82nd.
Alba then turned victory into a rout on the break with Milan entirely thrown into attack. – Sapa-AP