Liverpool's Champions League campaign ended in disappointment as Real Madrid set up a semi-final meeting with Chelsea by keeping Jurgen Klopp's side at bay in a goalless draw at Anfield.
Real arrived at Anfield protecting a 3-1 lead from the first leg and while they eventually went through in relative comfort Liverpool will curse themselves for missing several glorious first-half chances.
Mohamed Salah shot straight at Real keeper Thibaut Courtois, who also saved well from James Milner, in the opening moments and shot over when he should have hit the target while Georginio Wijnaldum was also guilty of squandering an opportunity to at least apply pressure to Zinedine Zidane's side.
Real's best chance saw Benzema drive in a shot that was deflected on to the post, while Courtois was in action again to block Roberto Firmino's angled shot after the break.
Liverpool ran out of steam and ideas as the second half wore on, and Real defended with defiance and resilience to seal the win and set up a meeting with another Premier League side in Thomas Tuchel's Chelsea.
Meanwhile Manchester City are through to the semi-finals of the Champions League for only the second time after sealing victory over Borussia Dortmund in the last eight courtesy of comeback win in Germany.
Holding a 2-1 lead from the first leg, City found themselves needing to chase the tie when 17-year-old England international Jude Bellingham curled in a superb shot from the edge of the box.
Stung by the concession, the visitors threw everything they could muster at the German side, with Kevin de Bruyne smashing an effort off the bar before Mahrez saw a shot blocked on the line by the brilliant Bellingham.
The crucial breakthrough for City came early in the second half as Emre Can was penalised for handling in the box and Mahrez stepped up to fire his side ahead again in the tie.
Phil Foden sealed it, adding to the late goal he scored at the Etihad to give his side their first-leg lead with a fierce drive that found the Dortmund goal via the post.
"I am incredibly happy for this club, for this chairman and for the fans, everyone," Pep Guardiola told BT Sport after seeing his side seal reach the Champions League semi-finals for only the second time.
It is the first they will play in under Guardiola, having lost to Real Madrid in Manuel Pellegrini's final season in charge in 2015-16.
"It is the second time in the semi-finals, so it is not history in the club, but we start to build it," continued Guardiola, whose side flirted with elimination on away goals after Jude Bellingham's opener on Wednesday, before sealing the tie through a Riyad Mahrez penalty and Phil Foden's finish.
"We were brilliant, except for the first 10 minutes where they were good.
"I'm incredibly happy to be in the semi-finals, to be one of the best four teams in Europe, to be against big, strong teams and we will try to be good."
He added: "Now, I don't want to think for one second about PSG. I want to celebrate. Dinner with the staff and the team. I don't know which wine, it will be a good wine for sure."
City will face Paris St-Germain in the semi-finals, with the French side having eliminated holders Bayern Munich on Tuesday.