Alexis Mac Allister headed in the only goal but Madrid were grateful to goalkeeper Thibaut Courtois for keeping the score down.

Trent Alexander-Arnold was met with a hostile reception on his return to Liverpool as a late substitute and the home crowd roared the Reds over the line for what could be a turning point in their season.

Both sides are now tied on nine points from their opening four games of the league phase.

Liverpool had lost six of their last eight games in all competitions, but stopped the rot by beating Aston Villa on Saturday as Arne Slot resorted to a more tried and trusted team selection.

Florian Wirtz replaced Cody Gakpo in the only change from the weekend and Liverpool again looked more like the side that stormed to the Premier League title last season.

Madrid had lost just twice in 20 games since former Liverpool favourite Xabi Alonso took charge but relied on Courtois to avoid a similar scoreline to their only previous defeat this season -- 5-2 at Atletico Madrid.

The Belgian broke Liverpool hearts when the sides met in the 2022 Champions League final with a man-of-the-match display as Los Blancos won 1-0 in Paris.

Courtois' busy night began when Wirtz teed up Dominik Szoboszlai who failed to beat the former Chelsea stopper from point-blank range.

Madrid were then rescued by a VAR review that deemed Aurelien Tchouameni's arm was in a natural position as the Frenchman blocked a shot inside his own box.

Courtois was tested once more by a thunderous Szoboszlai shot as Liverpool pushed for the opener.

It took 45 minutes for Madrid's star-studded forward line to muster a shot on target when Jude Bellingham jinked clear inside the box and fired a low effort that Giorgi Mamardashvili blocked with his feet.

Courtois continued to defy Slot's men in a blistering start to the second period as he clawed away powerful headers from Virgil van Dijk and Hugo Ekitike before denying Szoboszlai once more from a free-kick.

It took the English champions an hour, but finally the giant Madrid number one was beaten when Mac Allister powered in a header from Szoboszlai's free-kick.

A mural of Alexander-Arnold next to Anfield was vandalised in the hours before the game.

He was met by a chorus of boos nine minutes from time when he entered for his first appearance since September 16 after a hamstring injury.

Kylian Mbappe's scintillating form has been the major cause for Madrid's fine start to the campaign.

The French striker had only failed to score twice in 17 previous games for club and country.

Mbappe spurned the visitors best chance to level when he skewed wide from the edge of the box.

Vinicius Junior was also well-marshalled by Alexander-Arnold's one-time deputy Conor Bradley as the Spanish giants failed to score for the first time this season.

Courtois produced one last fine stop from Gakpo to ensure a nervy finale.

But Liverpool's much-criticised defence stood firm for their first Champions League clean sheet of the season.