The Rossoneri had struggled so far under new coach Paulo Fonseca, but were boosted by a 4-0 victory over Venezia on Saturday and the return of Alvaro Morata, Fikayo Tomori and Davide Calabria from injury. Malick Thiaw, Ismael Bennacer, Alessandro Florenzi and Marco Sportiello were still out of action. Liverpool won their first three matches under Arne Slot, but lost to Nottingham Forest at the weekend and made changes.
The Reds wore black armbands after one of their fans was killed in a car accident in Bergamo this morning on his way to the game.
See how the game unfolded on the Liveblog.
After the offside trap caught out Tijjani Reijnders, Milan took the lead within three minutes when Christian Pulisic completed a give and go with Morata to sprint down the right and place the angled drive beyond Alisson Becker.
Mike Maignan had treatment on his right knee, but was able to continue, while Mo Salah was unlucky not to equalise on 17 minutes when smashing a right-foot strike against the crossbar.
It was a warning and Liverpool equalised when Ibrahima Konaté jumped for a glancing header on the Trent Alexander-Arnold free kick, Maignan getting the timing all wrong on his attempted punch.
Diogo Jota failed to make the most of a Pulisic error by firing wide of the near post, then Maignan parried the Gakpo angled drive and was rescued by the crossbar again on the Salah follow-up.
Maignan got down to palm a Salah counter-attack round the base of the upright, but Liverpool were dominating after that bright Milan start and turned the game around. It was an almost identical goal to the first, a Kostas Tsimikas corner finding Virgil van Dijk's relatively free header after shaking off Reijnders.
Maignan kept the scoreline down by pushing a Gakpo curler round the far post, then straight after the restart was brave rushing out to deny Diogo Jota, with Tomori crashing into him in the process. That caused a cut to his left knee and he had to make way for 19-year-old Lorenzo Torriani.
Morata had penalty appeals rejected when going over Gakpo's knee, while Torriani made a save with his chest on Dominik Szoboszlai, Tsimikas scuffing the rebound wide.
Just as Milan were pushing forward, they gave the ball away cheaply and were punished on the counter-attack, Szoboszlai bundling over the line from a Gakpo cross.
Tammy Abraham did not make the most of an error as Alisson Becker came flying out for a poor clearance, while Ryan Gravenberch ran back to make a decisive block on the Rafael Leao pull-back from the by-line.
Tomori sprinted to deny Darwin Nunez on the rapid counter, but Milan had a triple chance late on with Pulisic and Reijnders shots charged down, Theo Hernandez firing the third just wide.
There was time in stoppages for Italy international Federico Chiesa to make his Liverpool debut after the transfer from Juventus. The home fans showed their anger by leaving early and chanting insults calling for the players to show some guts.
Rafael Leao thumped a strike against the near post with the last kick of the game, but it did little to calm the protest from the Milan supporters.
Pulisic 3 (M), Konaté 23 (L), Van Dijk 41 (L), Szoboszlai 67 (L)