Messi's superb double set Barca on their way in the first half at a raucous but desperately tense Nou Camp and David Villa and Jordi Alba struck after the break to send the La Liga side through to the quarter-finals 4-2 on aggregate.
They became the first team in Europe's elite club competition to ever overturn a two-goal first-leg deficit without the benefit of an away goal and are one of only five sides to fight back from more than one goal down.
"We will remember this for years to come," Barca sporting director Andoni Zubizarreta told Spanish television.
"Messi's two goals put us in a strong position, Villa's was very important and Alba gave everyone exactly what they wanted with the fourth," added the former Barca and Spain goalkeeper.
There was talk of the end of an era after a poor run of form saw Barca eliminated from the King's Cup and beaten in La Liga by arch rivals Real Madrid following the reverse to Milan at the San Siro last month.
Barca's dream of a third European crown in five years appeared to be in tatters and the pressure increased when Jose Mourinho's Real marched past Manchester United into the quarter-finals last week.
Messi, Champions League top scorer the past four seasons, was accused of failing to perform on the big occasions but proved on Tuesday against Milan that it was folly to question his form.
The Argentina forward and four-times World Player of the Year conjured the fifth-minute opening goal with a sweet curling strike with barely any back lift as a cluster of Milan players attempted to close him down.
His second came five minutes before halftime when he received the ball from Andres Iniesta on the edge of the area, created space for himself and lashed the ball past Milan goalkeeper Christian Abbiati.
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.
He has scored 40 goals in La Liga this season to help Barca move 13 points clear at the top and has 53 in 42 appearances in all competitions, including seven in the Champions League.
For all Messi's brilliance, Tuesday's match should be remembered as a superb team effort.
Playmakers Xavi and Andres Iniesta provided creative spark, Sergio Busquets was immense in central midfield and Alba and fellow fullback Daniel Alves gave Barca the width and penetration they lacked in the first leg.
Assistant Barca coach Jordi Roura, standing in for Tito Vilanova while he has cancer treatment in New York, will also be delighted that his decision to deploy Villa up front alongside Messi and Pedro paid off so handsomely.
Although he saw relatively little of the ball, the Spain striker was a handful for Milan centre backs Philippe Mexes and Cristian Zapata, helping create space for Messi to exploit, and his goal was beautifully taken.
The 31-year-old has struggled for form since returning from a broken leg sustained at the end of 2011 but responded with a finish that suggested he may be getting back to his best.
"It's a tremendous joy," Villa told reporters. "We should enjoy this and right now I don't care about our opponents in the quarter-finals."
"When you have days like this you forget all about the bad ones. I prefer to think about today. It is something we deserved and now we have to think about the future."
The draw for the last eight will be made on Friday, with Real, Juventus, Paris St Germain, Borussia Dortmund and Galatasaray already through along with Barca.