Real remain three points clear of Atletico but Barcelona moved to within a point of the leaders as they beat Almeria 4-1 yesterday.
Karim Benzema had fired Real into a third minute lead when he converted Angel di Maria's cross.
However, despite being denied what appeared a penalty when Sergio Ramos seemed to trip Diego Costa, Atletico were in front by half-time thanks to fine strikes by Koke and Gabi.
Another turned down penalty appeal saw Atletico assistant boss Mono Burgos sent to the stands as he tried to confront the referee midway through the second-half.
More From This Section
"I think we can leave here reinforced, we have drawn a game in which we were losing," said Real coach Carlo Ancelotti.
"The reaction of the players was good, in general we can be satisfied because Atletico Madrid are a very good team, especially at home.
"We are still three points ahead of them and we are leaders."
Atletico captain Gabi was understandably left enraged as his side missed out on a possible return to the top of the table.
- Home fans angry -
===================
"It was a very open game with chances for both teams but I am proud of Atletico Madrid.
"We wanted to offer this intensity and desire to the fans and I think that is what we did."
Ancelotti's men came into the game full of confidence after thrashing Schalke 6-1 on their return to Champions League action in midweek and took just three minutes to open the scoring.
A short corner from the right was worked back to Di Maria and his in-swinging cross was slotted home at the back post by Benzema.