Trailing 3-1 from the first leg of their quarter-final at Stamford Bridge, goals from Mason Mount, Antonio Rudiger and Timo Werner saw holders Chelsea at one stage leading 3-0 on the night and 4-3 on aggregate, on the verge of a famous European comeback.
However, substitute Rodrygo levelled ten minutes from the end of normal time before Benzema – scorer of a first-leg hat-trick a week ago – headed his 38th goal of the season to send the 13-times winners into the last four.
Carlo Ancelotti made just one change to the side that had started the first leg as Nacho replaced the suspended Eder Militao in defence, while Thomas Tuchel handed starts to Ruben Loftus-Cheek and Mateo Kovacic as he bolstered the midfield that had been so overrun at the Bridge, with Reece James and Marcos Alonso given the nod as full-backs in a back-four.
The Blues were in need of a fast-start and Mount provided it as he took advantage of a fortuitous break off Werner to lash a superb finish past former Chelsea ‘keeper Thibaut Courtois.
The visitors were much the better side and were level in the tie soon after the interval as Rudiger’s powerful header left Courtois no chance, though Real Madrid were furious with the award of a corner after James’ strike appeared to go wide without a touch from Luka Modric.
Marcos Alonso looked to have completed the turnaround with a thumping right-footed strike but the effort was chalked off by VAR for a handball by the Spaniard in the build-up.
Instead, it was Werner who put Chelsea ahead for the first time in the tie, showing great composure to shimmy inside two challenges, Courtois’ touch not enough to deny the German as his effort trickled wide of Ferland Mendy on the line.
Within five minutes, however, the home side had responded as Rodrygo volleyed home from Luka Modric’s outrageous, outside-of-the-boot ball to force extra-time.
Moments after Alonso’s disallowed effort, Benzema had headed against the woodwork when well-placed but the ruthless streak that downed the Blues in London returned in extra-time as he took advantage of Rudiger’s slip to finish from Vinicius Junior’s cross and set up a semi-final meeting with either Manchester City or rivals Atletico Madrid.