Correa equalised for Atletico in a breakaway five minutes into added time with a goal that was initially disallowed for offside but was awarded after video review. Éder Militão had given Madrid the lead in the 64th.
Sunday's draw left Madrid in second place, three points behind leaders Barcelona, who lost 4-2 to Osasuna on Saturday to end its seven-game winning streak. Atletico were third, two points behind Madrid after eight rounds.
"I always think positively," Madrid coach Carlo Ancelotti said. "We moved closer to the leader and we have been playing well."
The derby was interrupted shortly after Madrid's goal at the Metropolitano, with the referee sending the players to the locker rooms after Atletico fans kept throwing objects onto the field.
Militão had celebrated near the sideline in front of Atletico fans, and Madrid goalkeeper Thibaut Courtois was seen appearing to provoke Atletico fans after Militão scored.
"What the fans did wasn't right but we are not helping when we provoke them," Atletico coach Diego Simeone said. "I'm not justifying what the fans did, but we need to help as well."
It was Courtois who alerted the referee about the objects - including lighters - being thrown onto the field.
Atletico defender José María Giménez and midfielder Koke Resurrección went to talk to the fans in the section behind Courtois' goal. That section is where usually the more radical Atletico supporters are located. Atletico coach Diego Simeone also asked several times for the fans to behave.
A message over the stadium tannoy said the match was being interrupted for 15 minutes, and that it would be suspended if the problem continued.
The interruption came a day after the Spanish league said it would ask police to act against the promoters of a social media campaign which the league said was aimed at promoting racist acts against Madrid star Vinícius Júnior at the derby.
The social media campaign was based on a hashtag encouraging Atletico fans to wear face masks, apparently to make it more difficult for authorities to identify individuals who participate in racist chants or insults.
Social media videos showed Atletico fans before the match chanting "Vinícius is different."
Vinícius occasionally clashed with Atletico players at the Metropolitano.
Fourth-place 10-man Athletic Bilbao conceded a stoppage-time equaliser in a 1-1 draw with Sevilla at home, while Giovani Lo Celso scored an 85th-minute goal in Real Betis' 1-0 home win over Espanyol.
Iago Aspas got an 81st-minute equaliser for Celta Vigo in a 1-1 draw against visiting Girona.
