Thomas Tuchel's side will meet Manchester City in Istanbul after a fully deserved triumph at Stamford Bridge, secured through Timo Werner and Mason Mount.
The Germany international's first open-play goal in the competition since September 2019 put the Blues ahead before Mount converted from close range in the closing stages after the hosts had missed a plethora of second-half openings as they countered Madrid with ease.
Zinedine Zidane's men looked out of sorts in a makeshift 3-4-3, even with captain Sergio Ramos and former Chelsea star Eden Hazard back in the side, as their winless record against the Premier League club stretched to five matches.