The two sides went into the break on level terms after Fikayo Tomori's close-range opener following a corner was cancelled out by Mohamed Salah, who in the process netted his 20th goal in all competitions this season.
Divock Origi, fresh from his winner at the weekend, made it 2-1 in the early stages of the first half as the Reds ultimately cruised to a comfortable win to take maximum points in the group.
Liverpool will find out who they face in the first round of the knockout stages on Monday, December 13, with the last-16 kicking off in mid-February 2022.
Jurgen Klopp involved both Mohamed Salah and Sadio Mane from the off in somewhat of a surprising move, although the boss named eight other changes including the likes of Neco Williams, Nathaniel Phillips, Tyler Morton, Takumi Minamino and Divock Origi.
Liverpool made an assured start to the game as a well-worked combination between Salah and Williams saw the latter have a sighter at goal from the outside of the box, but the full-back's left-footed shot went straight into the arms of goalkeeper Mike Maignan.
There were no real chances to speak about for either side in the early stages, although the Reds enjoyed the greater share of possession in the hosts' third.
Liverpool began to look threatening going forwards as the half wore on, particularly through Williams and Salah down the right, whilst Alex Oxlade-Chamberlain had an effort blocked from outside the box before Ibrahima Konate headed wide from a corner.
Konate did well at the other end of the pitch to thwart Zlatan Ibrahimovic after the Milan striker had found space inside the box, with the Frenchman ushering Ibrahimovic away from the goal before intercepting his cross.
But Milan took the lead from the ensuing corner as Minamino missed his clearance at the near-post, forcing Alisson to palm into danger and allowing Fikayo Tomori to slam the ball home from close range and make it 1-0.
Milan's lead didn't last long, however, as Salah scored for a record-equalling seventh consecutive Champions League away game. Oxlade-Chamberlain's powerful drive was parried by Maignan towards the Egyptian, who made no mistake with a fine finish to slot the ball home.
Milan had a penalty shout early in the second half as Tsimikas came across Franck Kessie inside the box, but both the referee and VAR adjudged the challenge to be fair, much to the annoyance of Stefano Pioli's side.
The Reds went ahead just a few minutes later as a mistake by Tomori allowed Mane to nick the ball and get a strike off on goal, with Maignan keeping the ball out but punching directly towards Origi, who accepted the opportunity and powerfully headed home to make it 2-1.
With Atletico taking the lead in the other group game of the night and putting themselves ahead of Milan in the table, all the pressure was on the hosts to pull themselves back into the game.
But the Serie A side struggled to mount an immediate response, with the Reds controlling the ball well and looking to finish the game off with a third.
Joe Gomez and Naby Keita both returned to action from their respective injuries just after the hour mark as the duo replaced Salah and Mane. Keita slotted into midfield and Gomez went to right-back, with Minamino and Williams joining the attack.
The substitutions undoubtedly had an effect on Liverpool's attacking verve, although they continued to look comfortable both with and without the ball against a passive Milan side.
Origi then made way for Fabinho in the final ten minutes as Klopp looked to shore up his midfield, with Oxlade-Chamberlain - who suffered a knock earlier in the half - pushing up to a false nine position.
Kessie had a glorious chance to level the scores as he found himself in behind the Reds defence, but Alisson closed the gap brilliantly as he smothered the Ivoirian's shot and kept Liverpool in front.
Conor Bradley and Max Woltman, both 18, came on in the closing stages in place of Williams and Minamino as the Reds saw out the remaining minutes and sealed a comfortable 2-1 win.
AC Milan: Maignan, Kalulu, Tomori, Romagnoli, Hernandez, Kessie, Tonali, Messias, Diaz, Krunic, Ibrahimovic
Liverpool: Alisson, N. Williams, Phillips, Konate, Tsimikas, Morton, Oxlade-Chamberlain, Minamino, Salah, Origi, Mane
MOTM: Alex Oxlade-Chamberlain