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Michael Carrick's side took the lead twice, through Harry Maguire (2) and Danish midfielder Patrick Drogba (51), but the Red Devils crumbled under Milan's pressure. Milan scored three goals from close range inside the penalty area before Ruben Loftus-Cheek added a fourth, securing the victory for Amorim against his former club.
Forward Marcus Rashford made his first appearance for United since returning from a loan spell at Barcelona, the Spanish champions.
Manchester United captain Bruno Fernandes missed a penalty for the second consecutive friendly, with goalkeeper Lorenzo Torriani making a brilliant save. This followed Fernandes' earlier miss against Leeds earlier in the week. From a Fernandes corner in the second minute, Harry Maguire headed home the opening goal.
Milan equalised after a defensive error allowed new signing Gonçalo Ramos, the Portuguese striker who joined from Paris Saint-Germain, to break into the penalty area and cross for Samuel Chukwueze to tap in (37).
United were awarded a penalty just before half-time after Belgian defender Kony De Winter fouled his compatriot Youri Tielemans. Fernandes took the spot-kick, but Torriani made a fine save.
The visitors regained the lead after Dorgho capitalised on a poor back pass from Filippo Terraccano (51), but Milan equalised again when Alvaro Cissé converted Chukwueze's poor shot at the far post (57).
Rashford, who had been sidelined by Amorim and first loaned to Aston Villa and then to Barcelona, came on as a substitute in the 60th minute.
Milan took the lead in the 68th minute when Ramos headed in Chukwueze's cross, and three minutes later, former Chelsea midfielder Loftus-Cheek scored Milan's fourth goal.
Portuguese manager Amorim was sacked as Manchester United manager in January after 14 months in charge, and was replaced by former Red Devils and England midfielder Carrick, who was given the job permanently after initially being appointed as interim manager.
Carrick led United to a respectable third-place finish last season.