With the 2021-22 LaLiga crown in hand, Carlo Ancelotti rested many of his starters from Real's incredible Champions League semifinal comeback win over Manchester City on Wednesday, including Karim Benzema, Thibaut Courtois and Vinicius Junior.
The hosts broke through near the end of a scoreless first half, when Matheus Cunha drew a penalty on Real Madrid's Nacho and Yannick Carrasco converted the spot kick to give Atleti a 1-0 lead at the break.
"It's a very important win today," said Atleti goalkeeper Jan Oblak, who made a number of good saves in the second half. "It was a very difficult game. Madrid are champions but they played well, they wanted the three points.
"We had a lot of chances in the second half but didn't finish off the game. Luckily we kept a clean sheet and one goal was enough."
Atleti had several opportunities throughout the second half to extend their lead, but Andriy Lunin, deputising for Courtois, made some key saves and Carrasco hit the post just after 75 minutes with only the keeper to beat.
Nacho had a chance to head Real level as full-time approached, but he failed to make good contact with a cross from Vinicius from a chance that the missing Benzema has made a habit of converting all season.
"Karim was tired, he hadn't recovered," Ancelotti said after the match. "The first thing I have to do is avoid problems. Luka [Modric] was a bit tired too, I preferred not to start him.
"The idea is to have the whole squad available on the 28th. [Luka] Jovic had some problems. We couldn't play out from the back, so the forwards had more difficulties than the rest."
The result keeps Real Madrid on 81 points from 35 games, while Atleti move up 64 points, six ahead of fifth-placed Real Betis in the battle for the final Champions League spot in LaLiga.
Oblak added: "Very happy with the three points in this fight for the Champions League, it's an important step."
"The boss picks the team," Vazquez said. "We go onto the pitch to do as well as possible. We have three games left and then the Champions League final, we'll have to work hard to win the trophy.
"The best way to prepare for the Champions League final is with these three games. In the Spanish league no game is easy."
It was a history making night for Diego Simeone, who notched his 10th victory over Real in 36 tries, passing Luis Aragones as the winningest Atleti coach in Madrid derby history.
"Football is complex," Ancelotti said. "We need to finish this season as well as possible. We have incredible fans, we've had an inconsistent season and they've always been with us. It was emotional today to see our fans, before the game. We have a responsibility to the fans and the club to maintain this level to the end.
"Ancelotti? Admiration. He's an extraordinary coach, winning five different leagues, and admiration for his personality. He's the same when he wins and when he loses. That's what makes you have admiration for Ancelotti."