The holders took the lead at Santiago Bernabeu thanks to a first-half tap-in from Karim Benzema, and with just over 25 minutes remaining, Marco Asensio extended their lead.
Real Madrid advanced in the Champions League after defeating 10-man Chelsea 2-0 in the first leg of their quarterfinal.
The difficult trip to Spain for Frank Lampard’s team was made worse by Ben Chilwell’s straight red card after he pulled down Rodrygo in the middle of the field.
Even if Carlo Ancelotti, the former manager of Chelsea, and his Los Blancos team will wish they had more to show for it, they will still go into the second leg at Stamford Bridge with a sizable advantage.
Within the opening 15 minutes, Benzema forced a close-range stop from Kepa and Thibaut Courtois stopped Joao Felix on the break.
But after 21 minutes, Benzema had the ball in the net as Kepa deflected Vinicius Junior’s attempt into his path.
David Alaba’s header five minutes before halftime nearly squirmed in as Real Madrid had chances to increase the advantage before the break.
Considerably before Kalidou Koulibaly was forced to limp off the field, Chelsea’s chances of mounting a comeback after the interval appeared bleak, and Ben Chilwell’s departure made it considerably worse.
Asensio then finished off another strong Real Madrid effort in Europe by sweeping home a cut-back pass in the 74th minute.
In the waning seconds of injury time, Benzema had a chance to make it three, and perhaps even should have, but he sent his looping header from nine yards out over the crossbar instead.
Although Ancelotti will be more aware than most that his team’s fight is far from finished, the hosts are currently on track to continue their outstanding continental record.