Thomas Tuchel's side wiped out Madrid's 3-1 lead from the quarter-final first leg as Mason Mount, Antonio Rudiger and Timo Werner put the reigning champions on the cusp of a stunning victory.
Then Luka Modric, 36, put all his skill and experience into one moment of genius as a sumptuous 30-yard pass with the outside of his right foot set up Rodrygo beautifully and the substitute volleyed in.
In extra time, it was the turn of Karim Benzema to deliver on the big stage again.
After scoring a hat-trick in the first leg to give Madrid a 3-1 lead, Benzema dashed Chelsea's hopes again, capitalising on a Rudiger slip to head in. Real secured a 5-4 aggregate victory despite a 3-2 loss on Tuesday.
“It was another incredible night at the Bernabeu,” said Modric. “We suffered but we never gave up. We kept fighting until the end and managed to advance. We gave everything we had and showed great character.”
Modric's moment of brilliance took social media by storm, with pundits and fans marvelling at its precision and execution.
Rio Ferdinand, on BT Sports, said: "This pass from Luka Modric is why I lost my voice today! That's illegal, that. Phenomenal."
Thierry Henry and Jamie Carragher also lauded the sensational move, which many have already labelled the pass of the year.
"It was another incredible night, what a sweet-tasting loss," Modric told Movistar Plus.
"We didn't give up until the end. Despite going 0-3, I don't think we played a bad game. Another night of suffering, but the important thing is that we have qualified."