Alexis Mac Allister and Cody Gakpo scored the goals in the second half as the Reds maintained their perfect record to return to the top of the table.
Mohamed Salah also fired wide from the spot, but it mattered little as Liverpool secured a 17th win in Arne Slot's first 19 games in charge.
Slot has already achieved what Jurgen Klopp could not as Liverpool boss by slaying the Spanish giants.
Liverpool had a score to settle with Madrid, who were unbeaten in eight previous meetings between the sides, including Champions League finals against Klopp's men in 2018 and 2022.
Defeat sends Carlo Ancelotti's side tumbling down to 24th in the table.
Only the top 24 progress to the knockout stage with the top eight advancing directly to the last 16.
Liverpool are well on course to do just that and the confidence coursing through a side also eight points clear at the top of the Premier League was in evidence throughout in front of a highly-charged Anfield crowd.
Madrid were hamstrung by a lengthy injury list and made the trip to England without Vinicius Junior, Rodrygo, Dani Carvajal, Eder Militao, Aurelien Tchouameni and David Alaba.
Young centre-back Raul Asencio has been pressed into action by those absences and he made a vital goal-line clearance on four minutes.
Darwin Nunez was sent in behind the Madrid defence by Salah and after his shot produced a fine save from Thibaut Courtois, Asencio reacted smartly to prevent the rebound bouncing off him and into his own net.
Courtois was Liverpool's scourge with a man-of-the-match performance in the final two years ago as Madrid prevailed 1-0 in Paris.
The Belgian was at his best again as he blocked another big Nunez chance from point-blank range as the Liverpool pressure built without reward before the break.
Courtois was in sparkling form again at the start of the second period to parry Conor Bradley's downward header.
Alexis Mac Allister fired Liverpool in front
Alexis Mac Allister fired Liverpool in front © Oli SCARFF / AFP
But Liverpool were not to be denied as Bradley was this time the provider for Mac Allister, who manufactured the space for a shot into the far corner on 52 minutes.
The visitors were relying on Mbappe for a moment of magic in the absence of Vinicius, but the Frenchman was well-marshalled by his international team-mate Ibrahima Konate and Virgil van Dijk.
His chance to silence his critics arrived on the hour mark when Andy Robertson was harshly adjudged to have tripped Lucas Vazquez inside the area.
Caoimhin Kelleher has excelled in the absence of the injured Alisson Becker and leapt to his left to save Mbappe's spot-kick.
Salah sparked a furore ahead of the game by declaring his disappointment with Liverpool's failure to offer him a contract renewal.
The Egyptian has been in sparkling form this season and his pace and trickery fooled Ferland Mendy into a mistimed challenge.
Salah, though, gave Madrid a lifeline by firing his penalty off the outside of the post.
Liverpool had to wait just six more minutes for the cushion of a second goal as substitute Gakpo rose highest from a corner to power a header past Courtois.
© 2024 AFP