Karim Benzema’s first-half goal had put Real fully in control against a timid Chelsea side led by Frank Lampard and the task become even greater when Chilwell saw red for cynically pulling Rodrygo back just outside the area when through on goal.
The match became a damage limitation exercise for Lampard’s side in order to stay in the tie for the return leg in London but Marco Asensio doubled the Champions League holders’ lead with a low strike that Kepa Arrizabalaga could not keep out.
Chelsea, who were denied a late Mason Mount goal by a brilliant block by former team-mate Antonio Rudiger, remain with an outside hope for next Tuesday’s second leg but will need to score at least twice to keep their season alive – something they have only done four times in their last 22 fixtures.
Lampard said: “Special things can happen at Stamford Bridge – we have to believe. I’ve been involved in nights like that.”
The winners will play Manchester City or Bayern Munich in the last four.