- Karim Benzema (78')
The UCL holders came into the match with a 5-2 advantage following the first leg at Anfield and a second-half goal from Karim Benzema sealed an outcome that most expected coming into the reverse fixture.
"It was a difficult game after the first leg, but from the start we wanted to go forward," Benzema said after the match. "It was a good game for the fans, for everyone, and we're in the quarterfinals."
Madrid looked more likely to score as the second half played out, with Federico Valverde heading just over the crossbar and Benzema missing a good chance before slotting into an open net from a Vinicius Junior assist to seal the tie for good.
Carlo Ancelotti's side is bidding to win back-to-back titles and a record extending 15th European crown, and Benzema said at this stage it didn't matter who Madrid faced in the next round.
"All the teams are good at this level, there are no small teams. It's about the small details, so we'll see who we get," Benzema said. "Football is about suffering. Everyone wants more, but sometimes you have to suffer. The most important thing is to win and go through."
In need of a three-goal win after losing 5-2 at home, Liverpool boss Jurgen Klopp picked a very attacking team with forwards Mohamed Salah, Cody Gakpo, Diogo Jota and Darwin Nunez in the starting lineup.
Nunez almost scored in the sixth minute after Salah stole the ball from Eder Militao and set up the Uruguayan, but his low shot was blocked by Courtois.
Playing with two disciplined four-man defensive lines and only Vinicius and Benzema up front, Real looked to counter-attack using the pace of the Brazil international down the left.
The inspired Vinicius almost scored in the 14th minute, but his point-blank volley was brilliantly saved by Alisson.
Courtois made several fine saves to keep out shots by Nunez and Gakpo, but Madrid stayed in control and seemed content to slow the pace of the game down to frustrate their opponents.
- Felix Zwayer