There were two controversial incidents in the first half at San Siro, as Milan wanted a penalty and Juventus protested there was a foul in the build-up to the Fikayo Tomori goal.
The Rossoneri went into the break leading 1-0 thanks to Tomori, but it was an eventful match with Rafael Leao hitting the woodwork twice.
There was controversy first when Dusan Vlahovic stuck out an elbow to block a Leao cross-shot, but although he clearly moved towards the ball, he was saved from a handling offence by having his hands clamped behind his back.
Theo Hernandez seemed to wipe out Juan Cuadrado when winning back possession and from the resulting corner, Milan took the lead.
VAR could not intervene in this case because the corner was an entirely new move, they would only have been able to call the referee back if the foul had been directly in the build-up to the goal.