The goal by Francisco "Isco" Alarcon just before halftime halted Atletico's onslaught and allowed Madrid to advance to its third final in four seasons with a 4-2 aggregate score following a 2-1 loss on Wednesday.
Earlier, the home support had made incredible noise as Atletico went 2-0 ahead through Saul Niguez's header and Antoine Griezmann's penalty, and had the holders on the ropes. Karim Benzema's sensational solo dribble on the left byline took out three Atletico defenders and he cut the ball back for Toni Kroos to drive a shot at goal.
Madrid need seven points from their last three league fixtures to clinch the title for the first time in five years and face Juventus in the Champions League final on June 3.
As it was, the damage from the first leg was irreversible as Real beat their neighbours in the competition for the fourth successive season.More news: Supreme Court Refuses to Hear Case on NC's Racist Voter ID Law
Zinedine Zidane's side lost 2-1 at Atletico Madrid last night but secured a 4-2 victory on aggregate, while Juventus comfortably dismissed French outfit Monaco 4-1. But Im with Real Madrid, another club of my life.
"I hope we will have him back before then, it is better that he plays a little bit".
To their credit Real Madrid remained calm and proceeded to dominate possession for the rest of the half, frustrating the home players and taking the sting out of Atleticos attacking thrust.
"After the game I asked Benzema how he was able to do that, but he didn't know either", Zidane said.More news: Why Boston should let LeBron James score 50 points a game
Dybala and Juventus have the chance to dethrone Zidane's defending champions Madrid at Millennium Stadium on June 3, but the Argentina worldwide heaped praise on the Turin favourite.
Simeone nearly left his job in despair following a penalty shootout defeat to Madrid in last season's Champions League final, but the Argentine struck a much more upbeat tone with his comments at the postmatch news conference at the Vicente Calderon.
"We played well against them this season so we've got a chance", the 30-year-old told Sevilla's official website.
However, the Spain global claims his stoppage-time goal against Chelsea in the semi-final of 2009 is his greatest moment in the competition.More news: Body dumped along Texas road after hearse stolen
"They have a great team and are in very good form".
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