It was only the shadow of brilliant Real keeper Thibaut Courtois that threatened to stop Liverpool getting what they merited, with a stunning individual performance that revived memories of how he defied them when Jurgen Klopp’s team lost the 2022 Champions League final in Paris.
The Belgian made a string of magnificent saves, including four from Dominik Szoboszlai and a remarkable reflex stop from Virgil van Dijk’s header, before even he was powerless to stop Mac Allister’s header from the Hungarian’s free-kick.
Liverpool’s narrow victory margin does not touch the sides of their domination from first whistle to last, these crucial three points pushing them into sixth place in the Champions League table, a standing that will put them in the last 16 without the need to resort to a play-off if maintained.
Szoboszlai and Mac Allister ruled midfield, while Florian Wirtz provided some of the subtle touches that made his name at Bayer Leverkusen. Hugo Ekitike was a constant menace.
Liverpool were, unlike so often this season, rock solid at the back as Kylian Mbappe was marginalised, delivering a dreadful, error-strewn display. Vinicius had been beaten by Bradley long before the end.
If it was a miserable night for Alexander-Arnold, it was not much better for Jude Bellingham, offered the Anfield stage to deliver a reminder of his class before England head coach Thomas Tuchel names his squad to face Serbia and Albania after excluding him last time.
He provided one moment of danger in the first half when he forced Giorgi Mamardashvili to save with his legs, but was otherwise anonymous as Real failed to establish any sort of stranglehold.
Bellingham conceded the free-kick in a dangerous position that led to Mac Allister’s goal, offering little as Real tried to force their way back into contention, although he was not alone there.
He offered words of sympathy to Alexander-Arnold: “Obviously, it is one of those things in football. The fans booing isn’t a reflection of how they feel about him.
“I think it is more to give their team the edge and throw him off a little bit. I am sure they’re appreciative of what he has done for the club.”
Alexander-Arnold, once an Anfield idol, probably could not wait to get back to his new Madrid home, while life for Liverpool suddenly looks much brighter ahead of Sunday’s meeting with Manchester City at Etihad Stadium.