
Former Inter Milan defender Milan Skriniar had put PSG ahead but their advantage lasted only three minutes before Rafael Leao netted an acrobatic equaliser and Giroud then sealed a precious victory just after the break in front of 75,649 at the San Siro.
Milan now have five points from four games in third behind second-placed PSG with six points. Leaders Borussia Dortmund have seven points after winning 2-0 earlier on Tuesday at home to Newcastle United who are bottom on four points.
The match in San Siro was played at a frenetic tempo in the first half with end-to-end action and, while the pace inevitably slowed in the second period, it was an absorbing clash in which Milan had to hold on at the end as PSG piled on the pressure.