Barcelona look set to meet their historical rivals in the final as they took a 2-0 first leg advantage over Real Sociedad in the other semi-final at the Camp Nou yesterday.
Atletico had beaten Real at the Santiago Bernabeu in last year's final, but the hosts quickly set about making amends for that defeat as Emiliano Insua deflected Pepe's effort into his own net after just 17 minutes.
Di Maria was involved again as Real all but secured their place in the final when his deflected strike 17 minutes from time was credited as another own goal by Atletico defender Miranda.
Defeat ends a 24-game unbeaten run for Atletico and they will need a remarkable fightback to retain their title in the second leg at the Vicente Calderon on Tuesday.
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Real boss Carlo Ancelotti hailed his side's performance as the best since he took over last summer.
"I am completely satisfied. We did everything well, we moved the ball with pace and were very aggressive without it. I wish the team could always play like they did tonight."
Atletico coach Diego Simeone, meanwhile, was left to rue his side's luck.
"I think Real Madrid played very well, but they scored twice with shots that hit our players on the body and went in.