Karim Benzema’s first-half tap-in put the holders in front at Santiago Bernabeu before Marco Asensio doubled their advantage with just over a quarter-hour to go.
A straight red card for Ben Chilwell after he tugged down Rodrygo in-between compounded a tough trip to Spain for Frank Lampard’s men.
Former Blues boss Carlo Ancelotti and his Los Blancos side will wish they had more to show but will nevertheless head to Stamford Bridge with a healthy advantage for next week’s return leg.
Thibaut Courtois denied Joao Felix on the break and Benzema forced a close-range stop from Kepa at the other end inside the first 15 minutes.
Benzema was in the place after 21 minutes, though, capitalising when Kepa parried Vinicius Junior’s shot into his path.
Madrid had chances to extend the lead before the break with David Alaba’s header almost squirming in five minutes before half-time.
Chelsea’s hopes of a comeback after the break felt slim even before Kalidou Koulibaly was forced to hobble off, and Chilwell’s dismissal only worsened matters.
Asensio then was on-point to cap another fine European performance from Madrid when he swept home a cut-back delivery in the 74th minute.
Benzema could and perhaps should have made it three in the final stages of injury time, only to push his looping header over the crossbar from nine yards out.
But the hosts are now well on course to extend their superb continental record, though Ancelotti will know more than most the battle is not over yet for his side.
What does it mean? Madrid move closer to semis
Things are never simple in the Champions League but for the hosts, the next step towards a successful title defence has been taken with minimal fuss.
Madrid look like they can go all the way again this season but they will know the job is only half-done despite their two-goal cushion.
Benzema extends English joy
Benzema found the back of the net once again when facing an English team in this competition, taking his tally to 20 goals.
Only Lionel Messi has netted more Champions League goals than the Frenchman against English sides, with 27.
Chelsea under the cosh
Despite a lively start, the Blues wilted under the heat of a fearsome Santiago Bernabeu crowd, with interim boss Lampard cutting a morose figure.
His side seldom appeared to be on the front foot, and the eight on-target attempts they conceded in the first half is a joint-worst figure on competition record for them.
Madrid travel to Cadiz on Saturday in LaLiga, while Chelsea host Brighton and Hove Albion in the Premier League on the same day.