Early goals by Diogo Jota and Sadio Mane, both created by Trent Alexander-Arnold, put the Reds in full command and there was no way back for the Spanish side once Felipe was sent off before half-time.
Jurgen Klopp's side should have dished out more punishment after the break but missed a flurry of chances and Jota had another strike ruled out for offside by the video assistant referee.
Atletico thought they had pulled a goal back from a deflected shot by former Reds striker Luis Suarez, but that too was chalked off for offside by VAR and they never seriously threatened a comeback.
As well as sending Liverpool through to the knockout stage with two games to spare, the win extends the Reds' unbeaten start to the season to 16 games.
In total, they have not tasted defeat for 25 matches, dating back to 6 April when they lost to Real Madrid in the quarter-finals of last season's Champions League.