Goals inside the first 21 minutes from Diogo Jota and Sadio Mane gave the Spanish champions a mountain to climb even before Felipe was sent off before halftime for a cynical hack on Mane.
Maximum points from four games are enough to win Liverpool group B and guarantee home advantage in the second leg of their last-16 tie come the new year.
Atletico, on the other hand, have to battle to reach the knockout stages as they sit third, one point behind Porto with two games to play.
When the sides last met at Anfield 20 months ago, Atletico's dramatic extra-time victory to reach the Champions League quarterfinals was overshadowed by the looming threat of coronavirus.
That proved to be the final top-level match in England for three months and the last in front of a full crowd for over a year.
The Liverpool support had not forgotten the bad blood that brewed between the teams from that tie and the Reds' 3-2 win in the Spanish capital two weeks ago.
Luis Suarez was roundly booed on his return to Anfield, while Atletico coach Diego Simeone was mocked as his side capitulated before halftime.
Liverpool manager Jurgen Klopp has not hidden his distaste for the cautious style Simeone's Atletico have become synonymous for.
However, the Argentine was aghast on the touchline at some of the visitors' defending during the first 45 minutes.
Just like their meeting in Madrid, Liverpool were 2-0 up inside the first quarter.
Jota easily escaped the attention of Felipe to have a free header from Trent Alexander-Arnold's cross to open the floodgates.
Alexander-Arnold was also the creator for the second goal as this time his shot was turned beyond Jan Oblak by Mane.
Alex Oxlade-Chamberlain then fired a shot inches wide as Liverpool threatened to run riot and Atletico lost their heads.