Teenage midfielder Warren Zaïre-Emery set up two goals, including PSG's third for South Korea winger Lee Kang-in near the end.
It was Lee's first for the club and a welcome win for PSG after it was routed 4-1 at Newcastle in the previous round, while seven-time champion Milan still has not won or scored in Group F.
PSG leads with six points from three matches and Milan is last. In other group game, Newcastle lost 1-0 at home to Borussia Dortmund.
Mbappé rifled a 32nd-minute shot past France goalkeeper Mike Maignan to give PSG the lead. Maignan was beaten again in the 53rd, when Kolo Muani tapped into an empty net after Maignan saved France winger Ousmane Dembélé's low shot following a short corner.
Milan coach Stefano Pioli picked a starting lineup without a single Italian player in it. According to OPTA statisticians, it was the first time in Milan's history that it had done so for a European game.
Midway through the first half, a spectator ran onto the field and hugged Mbappé, who seemed unfazed. The intruder evaded several security officials before getting escorted off.
Winger Rafael Leao shot just wide from outside the penalty area in the 26th and Mbappé did the same a few minutes later.
His next shot gave Maignan no chance, and the goal came following great work from the 17-year-old Zaïre-Emery.
He showed his strength breaking through midfield before picking out Mbappé, who junked right to put England defender Fikayo Tomori off balance before drilling a low shot into the left corner.
Kolo Muani's goal was much more straightforward as Maignan spilled the ball into his path after parrying Dembélé's snapshot from just inside the area.
Moments earlier, Dembélé thought he had scored his first for the club since joining this summer from Barcelona.
He broke down the right at great speed and arrowed a low shot into the left corner. But the goal was ruled out when a review showed Manuel Ugarte barging American midfielder Yunus Musah off the ball in the buildup.
Maignan expertly tipped Mbappé's curling shot onto the post late on but was well beaten when Lee struck a crisp shot past him in the 89th after swapping passes with Zaïre-Emery.
AP soccer: https://apnews.com/hub/soccer
Jerome Pugmire, The Associated Press