Seven-times European champions Milan, forced into the playoffs after finishing third in Serie A last season, were under huge pressure to reach the group stage and survived several scares from the Dutch side in the first half.
PSV, with an average age of just over 22 and four teenagers in the starting line-up, were unfazed by the imposing San Siro as they enjoyed more possession.
They nearly went ahead in the eighth minute when Tim Matavz's header was clawed away by goalkeeper Christian Abbiati and Milan took the lead with a low 25-metre shot from Boateng one minute later.
Abbiati made another important save to turn away Adam Maher's 30-metre volley and the visitors had two more chances just before halftime as Jetro Willems' looping cross hit the crossbar before Abbiati scrambled away another Matavz effort.
In between, Milan forward Stephan El Shaarawy rifled a shot against the underside of the crossbar before the ball bounced back into play.
Balotelli, Cup-tied from Milan's Champions League matches last season after his move from Manchester City in January, made the game safe in the 55th minute, diverting Philippe Mexes's flick into the roof of the net from close range.
PSV continued to play good football, only for Boateng to power into the penalty area and add a third with an angled shot in the 77th minute.
(Reporting by Brian Homewood; Editing by Ed Osmond Reuters Messaging: brian.homewood.thomsonreuters.com@reuters.net. To sign up for our Global Sports Forum chatroom, click on https://forms.thomsonreuters.com/global_sports_forum)
(Reporting by Brian Homewood)
