Casemiro put Real ahead with a volley but Antoine Griezmann equalised after scoring a one-on-one.
Atletico ended with 10 men after Thomas Partey was shown a second yellow.
Real coach Santiago Solari stated, “It was a team win and there's no other way to get something here against a solid and competitive side, particularly when they're playing at home. We were strong in every facet of the game. It's probably our best performance since December.
“It was a very complete display and that's the only way we were going to take anything here against a team who are better every year. They're a great side with a fantastic coach, we head home very happy. We were good at the back, up top, we pressed brilliantly and were solid on set-pieces, both offensively and defensively."