Stephan El Shaarawy's early header gave Milan the vital away goal ahead of next week's return in Italy, before Tim Matavz scored a deserved equaliser for PSV on 60 minutes.
Milan had been on the defensive during the early exchanges before Ignazio Abate got in behind Jetro Willems and won a tussle with the PSV defender.
Abate then delivered the ball to the unmarked El Shaarawy (15) to plant his header into the corner.
Before that opening goal, Adam Maher diverted an early cross inches wide of the Milan post, and had another effort from 25 yards pushed away by Christian Abbiati at full-stretch.
The PSV midfielder again forced Abbiati into action when the keeper blocked his angled volley from 12 yards, and Maher's frustration continued when he later blasted another shot off the upright.
El Shaarawy twice came close to doubling the lead in the opening seven minutes of the second half, dinking his first effort over Jeroen Zoet across the face of goal and later just failing to connect with Mario Balotelli's delivery to the back post.
PSV levelled on the hour when Jeffrey Bruma crashed a dipping shot from at least 35 yards which spun off Abbiati and Matavz (60) had the simple task of nodding the rebound over the line.
Karim Rekik should have given Eindhoven the lead 15 minutes from time when he lost his marker at a corner and headed wide from four yards.