In order to begin, to overcome a backward problem, Higuain – Cristiano Ronaldo's credit after his arrival in Turin – could have wished Wojciech Szczesny to miss a visit to his main club after hijacking him in the 41st minute.
The champions set a lead in the eighth minute with Mario Mandzukic, and Ronaldo's sealer secured the result nine minutes after his time.
A humanoid Higuain completed his personal horror show, angrily reacting when Juve's return from Manchester United's mid-week Champions League loss.
Their clean paper and a six-point lead on the top came up, though, watching Leonardo Bonucci from the bench where he spent 12 months.
It quickly eroded the confidence of Milan in a three-game Serie, with Mandzukic climbing over Ricardo Rodriguez and Alex Sandro's down-and-coming command of the cross.
Their misery has deepened just before Higuain, who was penalized by a VAR examination with Benatia's handballing, and who got out of it.
Szczesny has instructed his former team-mate to strike the loft and Higuain has let the goalkeeper keep a second penalty against Rossoneri.
Silent in the first half, Ronaldo forced Gianluigi Donnarumma into a smart stop shortly after rebooting, and the goal recovered in the 81st minute.
And after receiving a talk from the referee, Higuain had entered an early bathroom to grab a miserable night for himself and Milan.
What does that mean? Bianconeri good for break
They finally won comfortably and rarely defensive, but Massimiliano Allegri will still have the chance to take an international break after a completely non-fluent performance.
Szczesny stands up in San Siro
Higuain took a risk when he decided to pick up a man who had to face him on education several times. The decision backfired: Szczesny called insider information to move forward the decisive moment of the game.
Higuain drops Milan through a hole
It was clearly frustrating for Higuain, and its late melting leaves Gennaro Gattuso with greater results than this defeat. The Rossoneri boss now needs to focus on his attacking choices.
Milan's first match after an international break is a trip to Lazio, while Juve returns comfortably with a house fixture against SPAL.