Roma had failed to win either of their opening games this season, and their plight got even worse as they made the worst possible start here.
Marauding Milan midfielder Ruben Loftus-Cheek won a penalty after a VAR review showed he was clipped by Rui Patricio during a surging run into the box, leaving the evergreen Olivier Giroud to coolly convert from 12 yards - the Frenchman has now scored in six successive SA games.
The absence of Tammy Abraham and Paulo Dybala was clearly hurting the home attack who were struggling to create any danger in the final third, while they remained open at the back as Christian Pulisic almost scored for his third straight game, but his back-post volley was wonderfully tipped over the bar by Patrício.
While half-time may have given Jose Mourinho a chance to galvanise his side, any plans immediately went out the window as Rafael Leao scored an outstanding second for Milan two minutes after the restart.
The Portugal international appeared to be falling to the ground and off balance as a cross came to the far post, but he showed incredible skill to guide a volley back across Patricio and the ball crashed in off the post.
Although the Giallorossi were still struggling to force their way back into the game, they received a huge boost just after the hour mark when Fikayo Tomori was shown a second yellow card for a reckless challenge on Andrea Belotti.
That spurred Roma on, and helped by their numerical advantage, the hosts reduced the arrears in stoppage time.
Leonardo Spinazzola's effort took a wicked deflection off Pierre Kalulu, completely wrong-footing Rossoneri goalkeeper Mike Maignan to set up a very edgy last few minutes for Stefano Pioli's men.
There wasn't time for a second however, as Roma's disastrous start to the season continued - they've now failed any of their opening three Serie A games for the first time since the 2011/12 campaign, and Mourinho will be looking forward to the respite of upcoming the international break.
Milan have no such worries, with their 100% record intact as they kept up their status as the early season pacesetters in the race for the Scudetto.
Flashscore Man of the Match: Rafael Leao (Milan)
