The house group, with Frank Lampard within the dugout for a second spell, got here into the match at Stamford Bridge with kind and historical past towards them.
They began brilliantly, enjoying enterprising soccer, however missed two huge possibilities within the first half which might have put the strain on the defending champions.
Rodrigo scored within the 58th minute and the Spanish giants made Chelsea pay for his or her flamboyance as they doubled their tally with 10 minutes to go.
Chelsea, the 2021 European champions, have now misplaced all 4 of their matches since Lampard returned to the membership as caretaker boss instead of the sacked Graham Potter earlier this month.
Actual Madrid supervisor Carlo Ancelotti caught with the group that received the primary leg 2-0 final week, whereas Chelsea caretaker boss Lampard restored Reece James, Mateo Kovacic and N’Golo Kante to his line-up.
Regardless of their present woes, the house group, buoyed by an expectant crowd, received off to a superb begin towards the 14-time winners.
That they had an amazing probability to take the lead however Kante deflected his left footed shot from round 12 yards.
The guests, content material to bide their time, regarded sharp on the break.
Halfway by means of the opening interval, Rodrigo discovered house for himself and fired an effort towards the surface of the submit from an acute angle, though it was lined by goalkeeper Kepa Arrizabalaga.
Luka Modric examined Kepa with a shot from an angle and 5 minutes earlier than half-time Vinicius Junior deflected a shot from shut vary following a cross from the Croatia midfielder.
However Chelsea ought to have been forward on the stroke of half-time when Reece James fired a by means of ball from the best of the field and it fell to Mark Cukrella on the again submit.
The defender took a contact and shot however Thibaut Courtois flew by means of his personal objective to make the save.
Kante had one other golden probability to take the lead early within the second half, however his close-range effort hit Eder Militão and cleared away for security.
Lower than half an hour later, Actual took the wraps off Chelsea’s victory when Rodrygo scored from shut vary after an help from Vinicius.
Lampard made a number of attacking substitutions to get again into the match, bringing on Raheem Sterling, Joao Felix and Mykhailo Mudrić.
However Rodrygo scored once more within the eightieth minute after a intelligent help from Federico Valverde.
Actual Madrid will seemingly play Manchester Metropolis within the semi-finals, with Pep Guardiola’s facet main 3-0 towards Bayern Munich after the primary leg of their last-eight conflict.
However Chelsea are staring again on the closing weeks of a disastrous marketing campaign regardless of spending a staggering greater than £500 million ($621 million) within the membership’s first 12 months underneath new possession.
Already out of each home cups, they’re eleventh within the Premier League and look unlikely to qualify for European soccer subsequent season.
(With inputs from AFP)