Milan goalkeeper Mike Maignan was sent off for catching kneeing Genoa's Caleb Ekuba with his knee in the 97th minute and Giroud donned his gloves in a frantic finale.
Six minutes after that, Genoa goalkeeper Josep Martinez was also shown a red card for charging at Fikayo Tomori while trying to score from a corner.
That was 10 versus 10 and there were 113 minutes on the clock, but there was still time for some late drama as Genoa poured forward and Giroud came off his line to palm the ball away in a brave save under pressure from George Puscas.
Earlier, it looked like the game was heading for a 0-0 draw, but former Chelsea attacker Christian Pulisic gave AC Milan the lead after 87 minutes and the Rossoneri held on through all the late drama to win the game.
Olivier Giroud with a brilliantly brave save to secure the win for AC Milan! 😲 pic.twitter.com/z51fhB9HvrOctober 7, 2023
Giroud celebrated with his team-mates on the pitch after the win, which sees AC Milan move to the top of the table, where they sit with 21 points from their eight games so far.
Milan are two points clear of city rivals Inter, who were pegged back by Bologna after taking a 2-0 lead early on in their match on Saturday and had to settle for a 2-2 draw.
Juventus are four points back after beating Torino 2-0 in the Turin derby on Saturday. Defending champions Napoli can draw level with the Bianconeri with a win at home to Fiorentina on Sunday.
Also on Sunday, Roma travel to Cagliari in a must-win match for Jose Mourinho, whose job is rumoured to be under threat.
More Serie A stories
Napoli striker Victor Osimhen could be in for a January exit after he was mocked in a video online by his own club.
AC Milan have announced plans to move away from their iconic San Siro home and build a new stadium in the south of the city.
And Roma's Romelu Lukaku is being targeted by fans of former club Inter, who plan to hand out 50,000 whistles to show their 'disgust' when he returns to the San Siro with his current club at the end of this month.
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