Antoine Griezmann scored one of Atletico's goals to surpass Luis Aragonés as the club's all-time top scorer with 174 goals.
Madrid will play Sunday's final against either Barcelona or Osasuna, who meet on Thursday (Friday AEDT) in Riyadh.
Atletico took the lead with a header by Mario Hermoso after a cross by Griezmann six minutes into the match, but Madrid went ahead with Antonio Rüdiger scoring in the 20th and Ferland Mendy in the 29th.
Griezmann scored his milestone goal with a right-footed shot from outside the area in the 37th. Aragonés reached his mark in 370 matches, while Griezmann needed 368 games with the club.
An own-goal by Rüdiger in the 78th put Atletico ahead again before Dani Carvajal equalised in the 85th to send the game into extra time.
Atletico defender Stefan Savic found his own net while trying to intercept a cross by Carvajal in the 116th, and Brahim Díaz sealed Madrid's win in stoppage time by hitting the open net after Atletico goalkeeper Jan Oblak had left his area to try to score an equaliser the other way.
It was the first of three matches in less than a month between the Madrid rivals. They will also meet in the Copa del Rey and the Spanish league.
Atletico and Madrid also met in the 2020 final, with Madrid winning on penalties in what marked the first time the Super Cup was taken to Saudi Arabia in a lucrative multi-year deal for the clubs and the Spanish soccer federation.
It was a mostly quiet crowd during Wednesday match, and there seemed to be jeers during the moment of silence in honour of German great Franz Beckenbauer, who died this week.
The Super Cup's new "final four" format pits together the top two teams in the Spanish league last season and the last two Copa del Rey finalists.
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