Two goals by Milan forward Rafael Leao helped the defending champion fight back from a goal down and earn a 3-2 win over local rival Inter on Saturday in its fifth Serie A match of the season.
Tensions were running high as Milan defender Theo Hernandez and Inter midfielder Denzel Dumfries were handed yellow cards in the ninth minute after arguing following a collision.
Inter midfielder Marcelo Brozovic scored his first Serie A goal of the season in the 21st minute after an assist by forward Joaquin Correa following a brilliant counterattack orchestrated by forward Lautaro Martinez.
Milan, however, levelled seven minutes later through forward Rafael Leao, who slotted home past Inter keeper Samir Handanovic after collecting a pass from Sandro Tonali.
Stefano Pioli's side kept pressing but spurned a host of chances before the halftime whistle.
Milan forward Olivier Giroud completed the comeback in the 54th minute with a weak but effective strike as it caught Handanovic unprepared.
Leao scored his second goal after swiftly moving past the Inter defence and firing home in the 61st minute to extend the lead.
“Rafa has beautiful moves, plays beautifully, knows he has talent,” Pioli told reporters.
Inter did not go down without a fight, however, and scored just seven minutes later through forward Edin Dzeko, whose strike bounced off the post and slipped in.
Milan keeper Mike Maignan delivered a superb performance, keeping out further efforts by Inter which kept pressing until the end but was denied an equaliser.
"We conceded three goals, something you cannot afford in a derby. For the chances we had we should have deserved a draw," Inter manager Simone Inzaghi told reporters.
"We struggled a lot to score two goals this evening, and then we found in front of us a great goalkeeper."
Pioli also said Milan should not have relaxed in the last 25 minutes and should be grateful to Maignan for not conceding another goal.
"Until the 70th minute I liked the team a lot, they played with courage and fought with great determination," he added.
Milan tops the table on 11 points after five games and travels to Sampdoria next Saturday while Inter, fifth with nine points, hosts Torino on the same day.