Mikel Arteta's men, who beat Lyon 3-0 on the opening matchday, struck twice in the first half through Martin Odegaard and Reiss Nelson before Fikayo Tomori pulled one back for Milan 12 minutes from time.
The Gunners withstood late pressure from the Rossoneri to claim the three points needed to secure the friendly trophy, and they secured the additional point in the penalty shootout after Brahim Diaz and Rade Krunic failed to convert.
Arsenal welcomed both Ben White and Thomas Partey back to the first XI following the World Cup, but it was the Rossoneri who enjoyed the brighter start at the Al Maktoum Stadium.
In the absence of Zlatan Ibrahimovic and ex-Gunner Olivier Giroud, Divock Origi was chosen to lead the line, and the Belgian opened up space for a 20-yard shot in the 11th minute.
Origi's lovely flick took him away from Rob Holding, but his curling effort crashed against the bar before Arsenal began to cut out the sloppy mistakes and get a foothold in the game.
With 21 minutes on the clock, Odegaard taught Origi a lesson in long-range efforts, as he directed a brilliant free kick up and over the wall into the back of the net following a foul on the lively Eddie Nketiah.
Origi had another chance to make the net ripple in the 27th minute after a floated cross from Yacine Adli on the right, but the Belgian inexplicably headed wide of Karl Hein's far post from close range.
Arsenal needed no second invitation to take advantage of any Milan mistakes, as goalkeeper Ciprian Tatarusanu gave the ball away to Fabio Vieira in the 42nd minute after a dreadful attempt at a clearance.
Vieira drove forward before laying off Nelson, whose effort took a deflection off the studs of Odegaard on its way over Tatarusanu for Arsenal's second, but the Englishman was credited with the goal.
Milan piled the pressure on Arsenal early in the second period, but Hein was left untested in between the sticks, and Odegaard very nearly helped Arsenal score a third via another deflection off of the Gunners captain.
Long-shot specialist Mohamed Elneny let fly from a good 35 yards in the 59th minute, and the ball struck the top of Odegaard's head as he tried to duck out of the way, but the Egyptian's effort flew just over the bar.
Stefano Pioli's side would be rewarded for their persistence in the 78th minute, as Sandro Tonali's free kick from the left found the head of Tomori, who directed a bullet header into the bottom corner.
Arsenal survived seven minutes of injury time to secure the trophy-clinching win before having the chance to end the tournament with a perfect eight points in the penalty shootout, and Hein repeated his Lyon heroics with a low save from Diaz.
Cedric Soares, Ismael Bennacer and Gabriel Magalhaes had all converted before Diaz fluffed his lines, and Marquinhos sent Arsenal's next spot kick into the bottom corner for a 3-1 lead.
Tonali and Elneny both scored before Tatarusanu saved from Matt Smith to keep the tie alive, but Krunic sent his penalty wide to hand Arsenal another shootout win.
The Gunners now prepare to travel home for their final winter friendly against Juventus at the Emirates on Saturday, while Milan have two full days to recover before taking on Liverpool on Friday.