The World Player of the Year put Barca ahead with his first penalty after only 11 minutes, setting the competition scoring record for a season with his 13th goal of the campaign.
Antonio Nocerino pulled one back for Milan, who held Barcelona to a 0-0 draw in last week's first leg, but Messi restored the lead again from the spot just before the end of a breathless first half.
The majestic Argentine helped set up the third goal for Andres Iniesta after the restart and Barca closed the game down from then on to become only the second team to reach five consecutive Champions League semi-finals.
"We had to work very hard and we are very pleased to be in the semi-finals again," midfielder Iniesta told Spanish TV.
"Things are going very well. The team still has the ambition to go far and try to win trophies. It's exciting to be in the last four and let's see tomorrow who we'll get to play."
Barcelona will play the winners of the quarter-final tie between Chelsea and Benfica which the London side lead 1-0 going into the second leg at Stamford Bridge on Wednesday.
CRACKLING ATMOSPHERE
The game kicked off in a crackling atmosphere, Barca leaving three at the back and racing forward at every opportunity while Milan counter-attacked with pace and aggression.
Messi had already come close to scoring twice when Luca Antonini slid into the back of him in the area and bundled the Barca forward over for the first penalty.
Milan goalkeeper Christian Abbiati guessed right but the Messi's spot kick was tight in the corner.
The visitors looked to play long balls up to former Barcelona striker Zlatan Ibrahimovic, and it paid dividends when the tall Swede slipped a pass into the area for Nocerino to fire in the equaliser after 32 minutes.
Barca were awarded a second penalty when Alessandro Nesta pulled Sergio Busquets back by his shirt at a corner, and this time Messi sent Abbiati the wrong way from the spot.
Abbiati had made great saves to deny Messi and Xavi before the break, but he could do little about Barca's third.
Messi arrowed across the edge of the area and when his shot was blocked it broke to Iniesta, who showed great composure to dink it over the diving keeper.
"Barcelona is the best team around, we knew that," Milan midfielder Massimo Ambrosini told Italian TV. "I thought we started well but they played better in the second half. We played our cards and we come away without major regrets.
"We could maybe have done a bit more tonight but over the two matches I don't know how much more we could have done."
