The match took a dramatic turn when Milan's goalkeeper, Mike Maignan, was sent off in the 97th minute for a collision with Genoa's Caleb Ekuba. With no substitute goalkeeper available, Giroud stepped up as the makeshift keeper for Milan.
In a chaotic finish, Genoa's goalkeeper, Josep Martinez, also received a red card for his aggressive attempt to score from a corner, leaving both teams with 10 players on the field.
As the clock showed 113 minutes, Genoa pressed forward aggressively. In a courageous move, Giroud ventured off his line and made a vital save under pressure from George Puscas, securing Milan's victory.
The game had seemed destined for a goalless draw until former Chelsea player Christian Pulisic scored for AC Milan in the 87th minute.
With this dramatic win, AC Milan claimed the top spot in the league table with 21 points from eight games. They hold a two-point lead over city rivals Inter, who settled for a 2-2 draw against Bologna.
Juventus, following a 2-0 victory in the Turin derby against Torino, sits four points behind Milan. Napoli has the chance to catch up with Juventus if they win against Fiorentina on Sunday.
