Antoine Griezmann scored a club record-breaking 174th goal for Atletico and Rudiger netted an own goal before Carvajal forced extra time.

A late Stefan Savic own goal and Brahim Diaz strike won the game for Real.

Atletico keeper Jan Oblak had gone forward in injury time with Diaz beating him in a race starting in his own half before slotting into an empty net from 40 yards.

Real Madrid play either Barcelona or Osasuna - who meet in the other semi-final on Thursday - in Sunday's final.

If Barca win their semi it would mean a second El Clasico final in a row, with Barcelona winning 3-1 last year.

Griezmann made history with his excellent strike from the edge of the area after beating two defenders, overtaking legendary Luis Aragones as Atletico's all-time leading scorer.

But it was not enough for Diego Simeone's side, who were five minutes from the final before Carvajal's strike and four minutes from a shootout before Savic deflected the ball into his own net.

Atletico's next game is also against Real Madrid, with the capital rivals meeting in the Copa del Rey last 16 next Thursday.