Real Madrid ended Chelsea’s hopes of Champions League success this season and their likely prospects of playing in Europe next campaign by completing a deserved quarter-final win in London.
Down 2-0 from a one-sided first leg, the Blues put on a more positive show.
But 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 likely face Manchester City, who lead Bayern Munich 3-0 in their last-eight tie.
The loss for Chelsea extends the losing streak of Frank Lampard to four matches since he returned as Blues interim boss earlier this month.
Things could have been different had N’Golo Kante scored with a shot from an unmarked position early on or Marc Cucurella been able to find a way past Courtois at the back post late in the first half.
Kante was again denied after the break but, having committed men forward, they were decisively caught on the counter by Real as Vinicius Junior tore away to set up Rodrygo’s close-range finish.
The Brazilian then made absolutely sure of 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 points behind Brighton in seventh, Chelsea now need a near faultless run of form in the remainder of the season to qualify for European competition.