The Italian fumbled a long-range effort to gift Tim Matavz an equaliser after Stephan El Shaarawy had put the visitors in front in Eindhoven
Stephan El Shaarawy opened the scoring for the visitors after 15 minutes with a close-range header at the end of a flowing move.
Kevin-Prince Boateng released Ignazio Abate down the right-hand side and his pin-point cross was met by the striker, who headed powerfully past Jeroen Zoet.
PSV got themselves level on the hour as Matavz reacted quickest to head past Christian Abbiati after the goalkeeper had failed to hold a Jeffrey Bruma strike.
And despite late pressure, neither side could find a winner to give them the advantage heading into the second leg.
After being cup-tied for last season’s European campaign, Mario Balotelli was given his first start for Milan in the Champions League, joining El Shaarawy and Boateng in attack.
PSV coach Philip Cocu was dealt a blow in the lead-up to the game with the news that in-form striking starlet Zakaria Bakkali had been ruled out with a groin injury.
The 17-year-old – who has scored four goals in four games in all competitions this season – was replaced in the starting line-up by Matavz.
PSV started well, but having survived an early period of pressure Milan sprang into life in the 15th minute as El Shaarawy broke the deadlock.
The 20-year-old rose unmarked to head home Abate’s right-wing cross after some lax PSV defending.
The Dutch side sought a response, and with eight minutes of the half to play Adam Maher came close to levelling, only to see his shot rattle the crossbar.
The 20-year-old midfielder broke at pace towards the Milan defence before holding off the challenge from Cristian Zapata and firing in his shot, only for the woodwork to come to Abbiati's rescue.
Milan should have doubled their lead early in the second half but El Shaarawy missed two clear-cut chances after excellent work from Balotelli.
The striker saw his first chance bounce wide of Zoet after a delicate chip, and his second opportunity was denied by a perfectly-timed tackle from Jetro Willems.
Those misses proved to be costly as PSV equalised on the hour mark.
Bruma sent a speculative long-range effort towards goal and the ball bounced in front of Abbiati, causing it to strike him on the chest and loop into the air.
And before the goalkeeper could react, Matavz pounced to head the ball into the back of the net to put the Eredivisie side level.
On-loan defender Karim Rekik had a fantastic opportunity to win the game for PSV late on, but he mistimed his header following a perfect Georginio Wijnaldum cross, leaving the tie finely balanced ahead of the return leg at San Siro on August 28.