Sergio Ramos nearly snatched a win in injury time but his free-kick was brilliantly clawed out by Oblak to ensure that the points were shared in a result which leaves La Liga leaders Barcelona 11 points clear of Atletico with seven games remaining.
The Welshman was an unused substitute during Real's 3-0 Champions League win over Juventus on Tuesday, but comes in against Diego Simeone's men.
Kane: Tottenham's second goal should be mine
Christian Eriksen and Harry Kane canceled out Mame Biram Diouf's goal to earn Spurs the three points. Kane later tweeted: "Definitely claiming that goal, flicked off my shoulder on the way in".
The first opportunity of the match fell to Real Madrid in the ninth minute, but Ronaldo could not bundle the ball past Atletico goalkeeper Jan Oblak from close range after meeting a flicked header from Bale.
Real could have gone into the break with a one-goal lead but Marcelo saw his curling effort rattle against the crossbar two minutes before halftime.
Atletico made a sloppy start to the second half and were punished by Ronaldo.
Real Madrid's French coach Zinedine Zidane (L) cheers Real Madrid's Portuguese forward Cristiano Ronaldo as he leaves the field during the Spanish league football match between Real Madrid CF and Club Atletico de Madrid at the Santiago Bernabeu stadium in Madrid on April 8, 2018.
But it was skipper Sergio Ramos who nearly won it at the death when his free-kick looked to be heading into the top corner until Oblak got a hand to it.