Liverpool s Egyptian forward Mohamed Salah centres the ball during the UEFA Champions League Group B football match between AC Milan and Liverpool on December 7, 2021 at the San Siro stadium in Milan (AFP)
Liverpool made it a perfect six Champions League wins from six on Tuesday becoming the first Premier League side to achieve this feat.
Fikayo Tomori had given Milan hope they could make the last 16 with his tap-in just before the half hour mark at the San Siro but a quick reply from Mohamed Salah and Divock Origi's nodded finish 10 minutes after the break ensured Jurgen Klopp's side finished Group B on 18 points.
Serie A leaders Milan, who were missing half their starting back four and three other first team players including forwards Rafael Leao and Ante Rebic, failed in ther attempt to make the last 16 for the first time since 2013.
Stefano Pioli's side have looked an accomplished side domestically this season but were punished for picking up just one point from their first four group matches.
Klopp made a raft of changes from the Reds' side which squeezed past Wolves at the weekend but there was still a obvious gulf in class between the two teams.
Milan struggled to put a second-string Reds outfit under much pressure in the tame opening stages.
The closest either side came to scoring was a Tomori header in the eighth minute that Alisson Becker had no trouble saving, while Neco Williams' shot two minutes earlier dribbled into Mike Maignan's arms.
Out of nowhere the San Siro exploded into life thanks to Tomori's 29th-minute opener, which fell to him on a plate after Alisson could only pat the ball out to the England international.
However their joy only lasted six minutes as Salah netted his 20th goal of the season, pouncing after Alex Oxlade-Chamberlain did brilliantly to wriggle free and fire a stinging shot at Maignan.
And Milan's hopes of making it through all but vanished 10 minutes after the break as Origi looped home Liverpool's second on another rebound, this time from Sadio Mane's shot after Tomori gifted the Senegal forward possession on the edge of his own box.
From there Liverpool easily held off the home side, with Alisson rushing out to block Franck Kessie's finish when put clean through the only real danger Milan managed to pose with five minutes remaining.
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