AC Milan striker Olivier Giroud's powerful header early in the second half secured a 2-1 Champions League Group F home victory over Paris St Germain in a pulsating match on Tuesday for the first win in this season's competition by the Italian side.

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.

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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.

"It was a high-level match, we knew the difficulty of coming to play here," PSG captain Marquinhos told Canal+. "The second goal changes the match because we were good at that moment.

"We knew it [qualification for the knockout stages] would be hard if we didn't win today, but we must not give up. Everything remains in our hands."

Milan, who reached the semifinals of last year's competition, won a Champions League game in which they had trailed for the first time since beating Real Madrid in 2009.

PSG went ahead after nine minutes following a well-worked corner. Marquinhos flicked on the set-piece and Skriniar was left unmarked to head home his first goal for the Paris club.

They have scored in their last 48 group stage matches in the Champions League, the longest run in the competition's history, having previously drawn a blank against Real Madrid in 2015.

But the home side were level three minutes later with an excellent finish from Leao. Giroud's initial shot was saved by Gianluigi Donnarumma against his former club but as the ball looped into the air Leao produced an overhead kick.

Kylian Mbappe then found himself one-on-one with Milan goalkeeper Mike Maignan but scuffed his shot wide before Ousmane Dembele struck the crossbar with a curling shot from 25 metres.

There was less goalmouth action in the second period but Milan led early when Theo Hernandez's superb cross was met with a powerful trademark header by Giroud.

Lee Kang-In struck a post for PSG on a luckless night for the Parisians as their five-game winning run came to an end.

"The players played with their heart, with energy; it's what we wanted. We managed to work as a team against a great side," Milan coach Stefano Pioli said.

"The team worked well together, and deserved the win. Now we need to perform well against Dortmund and overtake them."

Milan host Dortmund on Nov. 28, when PSG welcome Newcastle.