Raul Asencio was immediately thrust into the limelight on his Champions League debut and came out unscathed, as Darwin Nunez raced forward and hit a shot that Thibaut Courtois palmed onto the centre-back, who cleared off the line.
While that proved to be a rare sight of goal in the first 20 minutes, there was certainly no lack of a competitive edge, with Asencio and Nunez getting booked for a tussle in the box before Virgil van Dijk made a statement with a shoulder barge on Kylian Mbappe.
Nunez continued to be heavily involved as he pounced on a loose ball in the box but was denied by the onrushing Courtois.
Conor Bradley then answered pre-match questions about how he would fare against Mbappe with a superb tackle on the Frenchman moments before Nunez headed agonisingly wide.
Shortly after, Luis Diaz saw his header punched away by Courtois and Curtis Jones fired over as the Reds kept probing, although Alexis Max Allister was booked for cynically stopping an Arda Guler run going the other way, meaning he will miss the next game.
Liverpool remained on the front foot after the restart with Eduardo Camavinga deflecting Jones’ attempt wide and Courtois getting down brilliantly to palm away Bradley’s header.
The Reds made their breakthrough moments after the latter attempt, as Max Allister played a one-two with Bradley and sent his shot teasingly out of Courtois’ reach.
Having not seen a shot on target all game, Caoimhin Kelleher remarkably outfoxed Mbappe from the spot in the 61st minute after Lucas Vazquez went down under pressure from Andy Robertson.
Mohamed Salah was also unsuccessful from the spot, smashing his attempt wide of the post having twisted Ferland Mendy inside out to earn the penalty.
Undeterred, Liverpool got their second goal six minutes later as Cody Gakpo rose highest to head in from Robertson’s cross, making sure that the Reds retained their perfect Champions League record this campaign to stay top of the standings.
They also inflicted a third consecutive European defeat for a faltering Real Madrid side that currently occupies 24th place - the last play-off position.