Stephan El Shaarawy gave Milan a 15th minute lead against the run of play but Tim Matavz replied for PSV on the hour.
Milan, playing their first competitive match this season and one of the most important, were quickly in trouble as PSV's Adam Maher nearly diverted a Matavz shot into the net and goalkeeper Christian Abbiati turned away Georginio Wijnaldum's low shot.
But with their first real attack Milan went ahead when Ignazio Abate got the better of a tussle with Memphis Depay and crossed for forward El Shaarawy to head in.
Striker Mario Balotelli hit the crossbar for Milan in the next attack before the visitors were again forced on to the back foot by PSV's incisive, attacking play.
Maher had a superb volley parried by Abbiati and struck the crossbar after a mistake by Abate as the hosts swept forward.
Milan started the second half brightly, with Balotelli setting up two openings which El Shaarawy failed to convert, before PSV, who have won all five previous matches this season including their three domestic league games, levelled.
Abbiati was unable to hold Jeffrey Bruma's vicious long-range drive and Matavz headed in the rebound.
PSV then missed a glorious chance to win the game as 18-year-old defender Karim Rekik headed wide from an unmarked position six metres from goal, leaving Milan with a slight advantage for next week's return at San Siro.
(Writing by Brian Homewood in Berne; Editing by Ken Ferris)
