The visitors' defence proved unbreachable as Zinédine Zidane's men protected their first-leg lead.
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Real Madrid produced a defensive masterclass as they earned a quarter-final goalless draw at Anfield to see them through 3-1 on aggregate against Liverpool.
Match in brief
Liverpool, as expected on home soil, made the early running with Thibaut Courtois denying Mohamed Salah inside two minutes then repelling James Milner's curling effort.
Karim Benzema's deflected drive struck the post from a rare Madrid counter before Georginio Wijnaldum blazed over another presentable chance for the hosts before the break.
Courtois was forced into action by Roberto Firmino at the start of the second period but, in truth, the Belgian goalkeeper was seldom troubled thereafter as Zinédine Zidane's well-drilled defence quelled Liverpool's advances and booked a semi-final tie with Chelsea.
Man of the Match: Casemiro (Real Madrid)
"A controlling influence in central midfield. Protected the two centre-backs and was very good in transition from defence into attack."
John Peacock, UEFA Technical Observer
Matthew Howarth, Liverpool reporter
Liverpool had enough opportunities to stage another memorable Anfield fightback but – not for the first time this season – their cutting edge deserted them. They can have no complaints over two legs, though. Real were simply too strong for Jürgen Klopp's team and deserve their place in the last four.
Joe Walker, Real Madrid reporter
As professional as it gets from Madrid, who were rarely tested by a Liverpool side profligate throughout. The first-leg performance was more than good enough to see the 13-time winners through and you have to say that playing this way, you'd be brave to bet against them making it 14.
Casemiro, Real Madrid midfielder: "We knew we had the first-leg advantage but we played to win. They played with a lot of intensity. They've got a great team and coach but we worked hard. We didn't rest on our laurels, and that's ultimately what decided it."
Nacho, Real Madrid defender: "We knew we had the first-leg lead but they pushed, forced us back and had chances. But our team were so good in defence. Maybe we weren't as good as we'd have liked going forward but when you're 3-1 up from the first leg this kind of approach is normal. People said we weren't favourites against Liverpool, and now we've got another tough side in the semis, but we are confident and we want to get to another final."
James Milner, Liverpool midfielder: "We played well but when you don't put your chances away, you get punished. The intensity and drive was there but it wasn't enough in the end. They're obviously an experienced side, a top side, but the tempo was there from us today. We just couldn't put away our opportunities."
• Liverpool have won just two of their last 14 fixtures against Spanish clubs (D3 L9).
• This was only the second time the Reds had failed to score in 16 UEFA Champions League matches at Anfield.
• Madrid have now won 16 of their 17 UEFA Champions League knockout round ties when winning the first leg by two goals or more.
• The Spanish side will be in the UEFA Champions League semi-finals for a record 14th time.
• Madrid failed to score for the first time in 24 UEFA Champions League knockout phase games.
• Courtois made his 50th appearance in the UEFA Champions League (group stage to final).
Liverpool: Alisson Becker; Alexander-Arnold, Ozan Kabak (Diogo Jota 60), Phillips, Robertson; Milner (Thiago Alcántara 60), Fabinho, Wijnaldum; Salah, Firmino (Shaqiri 82), Mané (Oxlade-Chamberlain 82)
Real Madrid: Courtois; Valverde, Nacho, Éder Militão, Mendy; Kroos (Odriozola 72), Casemiro, Modrić; Asensio (Isco 82), Benzema, Vinícius Júnior (Rodrygo 72)
Madrid head to Getafe and Cádiz in the next seven days before a home game with Real Betis (24 April) as they aim to overhaul Atlético at the Liga summit. The UEFA Champions League semi-final ties are scheduled for 27/28 April and 4/5 May. Liverpool, meanwhile, must now focus on securing a top-four finish in the Premier League.