Watch Barcelona 3 vs AC Milan 1 Video Highlights
Messi gave Barcelona the lead when he slotted home past goalkeeper Christian Abbiati in the 11th minute of play.
Antonio Nocerino netted the equaliser for AC Milan in the 32nd minute before Messi scored again from the penalty spot – firing on the next side this time – in the 41st minute.
Spanish star playmaker Andres Iniesta then sealed the victory for Barcelona after 53 minutes.
The defending champions now awaits the winner of the Chelsea v Benfica game, which takes place on Wednesday.
AC Milan boss Massimiliano Allegri believes the Spanish side might have gotten a little help from the referee.
“Sometimes the referee made too many concessions,” Allegri said. “I don’t know if it proved decisive.
“We made a mistake on the first penalty but he helped on the second. Playing Barca is never easy.”
But Barcelona manager Pep Guardiola was delighted to see his team progressing, stating that they deserved their place in the semi-finals because they dominated over both legs.
“You can talk all you want about referees but that makes it five straight semifinals, the fruits of our talent and a lot of work,” Guardiola said.
“We deserved more than to just get through so I’m satisfied.”
In the night’s other game, the in form Bayern Munich beat Marseille 2-0 and 4-0 on aggregate.
Striker Ivica Olic, starting in place of Mario Gomez, who came on in the last 15-minutes – scored both goals for the German side, who faces Real Madrid or APOEL Nicosia.
Madrid, which have a huge lead from the first leg, are favoruites to progress.