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European champion Madrid had claimed a brilliant 5-2 win in England in the first leg of its last-16 tie, leaving Liverpool a mighty uphill battle in Thursday's (AEDT) return match.
The Reds defence – and Alisson in particular – at least gave their team-mates a platform from which to build this time, but the goal threat that had briefly concerned Madrid on Merseyside was less evident.
Eventually, Karim Benzema, that familiar foe, put Jurgen Klopp's side out of their misery as Madrid continued their bid for yet another crown in their favourite competition of all.
The goalkeepers were the undoubted stars of a goalless first half, with Alisson brilliantly blocking from Vinicius Junior at close quarters and soon touching Eduardo Camavinga's deflected shot onto the crossbar. A VAR review might have overturned the offside given against Vinicius when he was denied again by Alisson.
Those stops just about kept Liverpool in the tie, but Thibaut Courtois – the hero of last season's final between the sides – was not to be outdone. His fingertip stop from Darwin Nunez was as impressive as any of Alisson's saves, and he then beat away a thunderous Cody Gakpo drive.
Federico Valverde ran through early in the second half but scuffed straight at Alisson, with the same man heading over following excellent work on the left from Luka Modric. Benzema also missed the target when well placed on his right foot.
The chances continued to fall Madrid's way, however, and Benzema made no mistake when Vinicius miscued his finish and instead prodded to his team-mate for an open goal in the 78th minute.
Benzema took a kick in the process, but that was about the extent of Madrid's concern in a dominant 6-2 aggregate triumph.
