Atletico's jubilant fans spilled onto the streets of the Spanish capital to celebrate their first victory over their bitter city rivals in 14 years, while the Real faithful were left to reflect on a season without major silverware and the possible departure of Mourinho at the end of the campaign.
Ronaldo, who was shown a straight red card after he kicked out at Atletico captain Gabi in the second half of extra time, apparently catching him in the face, nodded Real ahead in the 14th minute.
Diego Costa levelled 10 minutes before the break and after Mourinho was dismissed for furiously protesting a referee's decision with around 15 minutes of regular time left Miranda glanced a 99th-minute header past Diego Lopez to secure a first win against Real since 1999.
After five minutes of nerve-wrenching extra time, the referee finally blew the whistle, sending the red and white-clad Atletico fans into raptures while the white half of Real's own stadium was left in mute shock.
The King's Cup does not carry the same prestige as La Liga or a European title but the Atletico fans' euphoria also reflected the fact that they had got the better of their city neighbours after more than a decade of disappointment.
"This team has worked extremely hard for this match," Gabi told Spanish television as his team-mates celebrated wildly and showered each other with champagne nearby.
"This victory tastes of glory and is for all those who have suffered for 14 years," he added.
After Ronaldo's opener and Costa's equaliser, Ozil struck a fierce shot against the post two minutes before the break and Karim Benzema was denied by the frame of the goal on the hour before Juanfran cleared Ozil's follow-up shot off the line.
There were further signs that it was not going to be Real's night when Ronaldo blasted a low free-kick against the post in the 69th minute and Michael Essien hammered the rebound over.
Centre-back Miranda nodded Koke's cross into the net to put Atletico ahead for the first time and Courtois conjured two stunning reflex saves to deny substitute Gonzalo Higuain and Ozil late into extra time.
"The team won with the hearts of each one of the players," coach Diego Simeone told a news conference.
"They lost their fear, as well as having the luck that you need," added the Argentine, who was playing for Atleti
