Real Madrid finished Chelsea's expectations of Champions League success this season and their possible possibilities of playing in Europe next campaign by completing a merited quarter-last win in London.
Down 2-0 from an uneven first leg, the Blues put on a more positive act.
Yet, Real's defence held firm before Rodrygo struck twice in the second half to win the leg and seal the tie.
In the semis, Real will probably face Manchester City, who lead Bayern Munich 3-0 in their last-eight tie.
The loss for Chelsea broadens the terrible dash of Frank Lampard to four matches since he returned as Blues in-between time boss recently.
The situation might have been different had N'Golo Kante scored with a shot from a plain position right off the bat or Marc Cucurella had the option to track down a far beyond Courtois at the back post late in the main half.
Kante was again denied after the break yet, having committed men forward, they were definitively gotten on the counter by Genuine as Vinicius Junior tore away to set up Rodrygo's short proximity finish.
The Brazilian then, at that point, ensured Real's win by tapping in after fine work from Federico Valverde to set him up in the box.
Sat 11th in the Premier League, 10 point behind Brighton in seventh, Chelsea presently need a close to perfect run of form in the rest of the time to fit the bill for European competition.