Olivier Giroud fired AC Milan back into Champions League contention with the decisive goal in Tuesday's 2-1 win over Paris Saint-Germain.

France striker Giroud thumped home a trademark header four minutes after the break at a pulsating San Siro to reignite Milan's chances of reaching the last 16 and turn around a dreadful recent run of form.

Stefano Pioli's team started the day bottom of Group F but are now well in contention for the knockout stages, third on five points and just one behind PSG who occupy the second qualification spot.

Tuesday's win was revenge for a 3-0 hammering in Paris a fortnight ago and came with Milan's first goals in the competition this season, the hugely impressive Rafael Leao drawing the hosts level in the 12th minute after former Inter Milan defender Milan Skriniar had nodded PSG into an early lead.

Giroud's winner was his seventh goal of the season in all competitions and there was a French flavour to the finish which downed Ligue 1 champions PSG, Theo Hernandez supplying the pinpoint cross from which his Les Bleus teammate netted.

"We showed everyone what kind of team Milan are at home," said Leao to Mediaset after being named man of the match.

"I am speechless but so proud of the team, we worked incredibly hard -- I am really happy."

Milan next host group leaders Borussia Dortmund, who took top spot by one point from PSG with their 2-0 win over Newcastle United earlier on Tuesday, in a match which could well be crucial to their chances of getting out of the group.

Their fans also got revenge on public enemy number one Gianluigi Donnarumma who controversially left Milan for PSG as a free agent two years ago and was greeted with a wave of hate from the packed stands.

A day which started with the news that a PSG fan had been stabbed in clashes between both sets of supporters late on Monday night reached fever pitch when the teams took to the field and home fans unloaded on Italy goalkeeper Donnarumma.

Milan fans printed thousands of fake dollar bills depicting his face with the word "mercenary" and the disparaging nickname "Dollarumma".

- Donnarumma hate -

They were launched onto the field after the traditional pre-match display amid loud, insulting chants towards Donnarumma which only got louder as he had to walk towards the goal nearest Milan's hardcore fans just before kick-off.

Some fans rolled the bills into hard balls and pelted them onto the pitch, where they pinged off the grass just by where he was standing.

It was Milan who should have taken the lead first when Ruben Loftus-Cheek smashed a great chance over the bar after Leao's blazing run and cut-back.

Skriniar had the away side ahead three minutes later after Loftus-Cheek allowed him to drift away and easily nod in Marquinhos' flick-on from a corner.

But Leao was clearly up for it after a series of underwhelming recent performances and another of his bursts brought Milan level almost immediately.

The Portugal winger charged down the middle, offloaded to Giroud and after his shot was parried by Donnarumma, flicked in the leveller with an acrobatic overhead kick.

PSG were dangerous on almost every attack and, after Mike Maignan had to twice be quick off his line to stop Kylian Mbappe, Ousmane Dembele thwacked the crossbar in the 27th minute.

Seconds later Giroud smashed into the side netting after Loftus-Cheek's powerful dribble in a breathless opening period, but he had his moment of glory with a classic centre-forward's header after Leao nearly poked home.

PSG were livid at what they thought was a foul on Achraf Hakimi from Leao, who was still on the ground when Giroud scored what turned out to be the winner.

Donnarumma denied Milan a more convincing victory when he brilliantly tipped wide Noah Okafor's angled drive with five minutes left.

And Lee Kang-in almost made Milan pay when he cut inside and slammed the post in a tense finale which ended with a massive roar of relief at the final whistle.