Real Madrid s French forward Karim Benzema celebrates after scoring a goal during the UEFA Champions League quarter final second leg football match between Real Madrid CF and Chelsea FC at the Santiago Bernabeu stadium in Madrid on April 12, 2022. AFP
Benzema had scored a hat trick in the first leg to give Madrid a 3-1 lead, then got the decisive goal at the Santiago Bernabeu Stadium with a header off a cross by Vinicius Junior six minutes into extra time.
The hosts had looked beaten after going down 3-0 in regulation, but substitute Rodrygo evened the aggregate score in the 80th and Madrid found a way to reach the last four for the 10th time in the last 12 seasons.
Chelsea had overpowered Madrid early and built a lead through goals by Mason Mount in the 15th, Antonio Rudiger in the 51st and Timo Werner in the 75th.
Madrid will next face either Manchester City or Atletico Madrid, which play on Wednesday in the Spanish capital with City defending a 1-0 lead from the first leg.
In the other quarterfinal on Tuesday, modest Spanish club Villarreal advanced past Bayern Munich 2-1 on aggregate after a 1-1 draw in the second leg in Germany.
The loss will add to Chelsea's off-the-field turmoil amid the forced sale of the club after sanctions in Britain against oligarch owner Roman Abramovich following Russia's invasion of Ukraine.
Chelsea sits in third place in the Premier League, five points clear of Tottenham in the final Champions League place with a game in hand.
Chelsea had eliminated Madrid 3-1 on aggregate in last year's semifinals en route to its second Champions League title.
The defending champions looked the more dangerous team during most of the match but both sides had opportunities in a high-intensity encounter that went back-and-forth toward the end of regulation.
Chelsea's American substitute Christian Pulisic had two good chances for a decisive goal in stoppage time but couldn't capitalize on them. The visitors also had a couple of opportunities later in extra time as they pushed for a goal that would take it to penalties.
The English side got a dream start when Mount opened the scoring after quick touches by Ruben Loftus-Cheek and Werner caught the Madrid defense off guard and left the forward with an easy shot from inside the area.
The visitors got the second with a firm header by Rudiger off a corner by Mount, and they thought they had another in the 62nd after Marcos Alonso scored from inside the area, but the goal was called back after video review because of a handball.
Instead, the third goal came when Werner scored from close range after a nice move to go past defenders in front of the net, but Madrid roared back five minutes later with a volley by substitute Rodrygo. It was set up by an exquisite pass by Luka Modric with the outside of his boot after Chelsea captain N'Golo Kante gave the ball away with a bad pass near the sideline.
Former Chelsea goalkeeper Thibaut Courtois had made a good save to deny an attempt by Kai Havertz a few moments earlier.
Benzema, who struck a header off the crossbar in the 66th, had been mostly contained as Madrid struggled to move the ball into attack and kept giving Chelsea opportunities.
Madrid couldn't play at the Bernabeu in the semifinals against Chelsea last year because the venue was undergoing major renovation work. Instead, the first leg was at the small Alfredo Di Stefano Stadium in the club's training center, a match that ended 1-1 before Chelsea won 2-0 in London.
Madrid played in the semifinals eight straight seasons before consecutive round-of-16 eliminations in 2018 and 2019. The loss in 2019 came against Ajax and was the last time Madrid was eliminated after winning the first leg. It was stunned 4-1 at home after a 2-1 win in the first match.
Madrid had stunned Paris Saint-Germain in the round of 16 this season behind a second-half hat trick by Benzema in the second leg at the Bernabeu.
Chelsea eliminated Lille 4-1 on aggregate in the last 16.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)