Alejandro Grimaldo and Jonathan David scored second-half goals for Atletico, which has moved them up to second place behind Barcelona.
Atletico scored twice in the second half to beat their city rival who played a man down nearly the entire second half at the Metropolitano stadium after Dean Huijsen was sent off in the 52nd for a foul that prompted the penalty kick converted by Grimaldo.
David added to the lead in the 59th, before Antonio Rudiger pulled one back for Real in the 89th.
Madrid wanted a red card for Atletico's Cristian Romero in the first half after he stepped on Jude Bellingham's leg.
The incident was reviewed by VAR but Romero was only shown a yellow card. Madrid also wanted a red card for Kang Lee-in for a hard foul on Federico Valverde.
Madrid coach Jose Mourinho lashed out at the refereeing after the match, saying there were "two clear red cards" for Atletico's players.
"The first half was tough," Mourinho said.
"It should have been nine (players) against 11, but in the second half it ended being 10 against 11 for them."
The result moved Atletico within five points of Barcelona, who won 3-1 at Sevilla on Saturday while Real Madrid dropped to third, six points behind Baracelona, who have won seven in a row to start the season.
Meanwhile, after two straight wins to start the Bundesliga season, newcomer Elversberg followed their loss to Bayern Munich with a 0-0 draw at promoted Schalke.
Also on Sunday, Miguel Gutierrez scored and assisted on Patrik Schick's goal as Bayer Leverkusen beat Leipzig 2-0 at home to move to fifth.
Napoli's mediocre start in Italy's Serie SA under Massimiliano Allegri continued after a 1-1 draw at Fiorentina.
Napoli havre only two wins from six matches in all competitions so far. Fiorentina had picked up their first points last week in its first match under Paolo Vanoli.
Juventus beat Atalanta 2-0 with goals from Francisco Conceicao and Gleison Bremer ending a two-game winless streak.
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