Karim Benzema struck for Real Madrid to clinch a 1-0 win over Liverpool and qualification for the Champions League quarter-finals on Wednesday 6-2 on aggregate.
After the wild last 16 first leg clash at Anfield in February left Madrid sitting pretty with a three-goal advantage, Liverpool coach Jurgen Klopp said his side only had a one percent chance of turning the tie around.
They stemmed the bleeding at the Santiago Bernabeu but never looked like mounting a stirring comeback of the type they managed against Barcelona in 2019, or AC Milan in the 2005 final.
Madrid have now knocked Liverpool out of the Champions League in three consecutive seasons, including beating them in last year's final.
"It was a complicated game but from the start we showed we wanted to go through, and we are in the quarter-finals," Benzema told Movistar.
"Suffering is part of today's football. Everyone wants more, but sometimes you have to suffer in a game – the most important thing is to win and go through."
The 14-time record winners showed the nous to keep Liverpool at arm's length, with defenders Eder Militao and Antonio Rudiger determined to shut out the visitors, along with goalkeeper Thibaut Courtois.
Reigning champions Madrid could have significantly stretched their lead, save for a series of superb stops by Liverpool stopper Alisson Becker and some unusually profligate finishing.
In the first leg, Madrid were lethal, with Vinicius Junior and Benzema netting twice each – neither were as decisive.
Yet eventually they combined for Madrid's winner after 78 minutes, with Vinicius slipping as he tried to shoot, but hooking the ball into Benzema's path for a simple tap-in.
Madrid's only worry was seeing their captain limp off after his goal amid an injury-hit season – Benzema said it was only a blow on the shin and Carlo Ancelotti confirmed he would be fit to face Barcelona in the Clasico on Sunday.
"Madrid were in control of the whole game, Ali had to make two sensational saves to keep us in the game," Klopp told reporters.
"Madrid were outstanding and that's why the better team went through to the next round."
Liverpool, deeply inconsistent in this campaign, took heart from their 7-0 thrashing of Manchester United in the Premier League, but could not produce the same magic under the Bernabeu lights.
Klopp started with Diogo Jota alongside his usual attacking trio of Mohamed Salah, Darwin Nunez and Cody Gakpo, deploying as much firepower as he could to try and mount a comeback.
The first chance of the game fell to Nunez but Courtois thwarted the Uruguayan, who was fed by Salah.
At the other end Madrid sliced open Liverpool on various occasions, and Alisson made a stunning save to deny Vinicius from point-blank range.
Eduardo Camavinga crashed a long-range effort against the crossbar, with Alisson getting his fingertips to it.
The Brazilian goalkeeper made further saves from Vinicius, Fede Valverde and Benzema as Madrid controlled the game.
Camavinga impressed in midfield and eventually helped create Benzema's goal, with a driven pass forward in the build-up.
"I told him a few small details, like how I know that the two Liverpool centre-backs play open, there's space in the middle, and that's how we scored the goal," added Benzema.
The striker has now scored seven times in the Champions League against Liverpool, more than any other player.
Benzema is key to Madrid's bid to lift the trophy for a sixth time in 10 seasons, if he can stay fit.
Madrid played classic Liverpool anthem "You'll Never Walk Alone" at the end of the game, at once a classy touch but also showing Liverpool never made them truly uncomfortable.
Ancelotti said Madrid were full of belief after their remarkable run to the final last season.
"We have a lot more confidence, because of what happened last year, it gave us a lot of confidence," said the Italian.
"We saw that in this tie, against a strong team, we did well in the two games.
"But later, with confidence alone, we don't reach the semi-finals. We have to play surprising football … as always, the Champions League is very complicated and we have to compete until the end."