World Player of the Year Messi ended his recent mini drought when he struck from the penalty spot after half an hour and midfielder Busquets netted a rare goal when he headed in a Xavi free kick 10 minutes later.
Milan pulled one back when Kaka’s low centre deflected into the net off Barca defender Gerard Pique moments before halftime before Messi raced through the middle to bag his sixth goal in Europe this season seven minutes from time.
The La Liga champions top the group on 10 points with Milan on five in second. Ajax are third on four points after they won 1-0 at home to Celtic in Amsterdam.
Barca quickly settled into their customary rhythm at their giant Nou Camp stadium with Xavi and Andres Iniesta pulling the strings in midfield and Messi, Neymar and Alexis Sanchez roving up front.
Alexis came close to an opener in the 21st minute when he just failed to get enough on a Neymar centre to turn it into the net before the referee ruled Ignazio Abate had hauled the Brazilian down in the area.
Messi, who had failed to score for four La Liga matches in a row before Wednesday, smashed the penalty straight down the middle and the familiar chant of the 26-year-old’s name echoed around the stadium.
Milan captain Riccardo Montolivo clipped a shot narrowly wide five minutes later but the visitors’ was caught napping when an unmarked Busquets headed into the net from Xavi’s free kick.
An impressive Kaka surge down the left wing led to Milan’s goal when his low centre skewed off Pique’s foot and past goalkeeper Victor Valdes into the net.
Milan coach Massimiliano Allegri brought Mario Balotelli on for Robinho at halftime and the Italy forward’s presence appeared to lift the Italian side.
They enjoyed a lot more possession without really threatening the Barca goal and Messi brought the supporters to their feet when he exchanged passes with substitute Cesc Fabregas and clipped the ball over Abbiati from close range to put the game beyond the seven-times European champions.
(Writing by Iain Rogers in Madrid, editing by Ed Osmond)