Neither team have been able to match runaway league leaders Barcelona this season, but the draw has seen Atletico remain four points clear of third-placed Real Madrid in second position.
Real Madrid boss Zinedine Zidane made four changes to the team that started against Juventus in the Champions League on Tuesday night. It was the same back five, but Lucas Vazquez, Mateo Kovacic and Marco Asensio all came into the midfield, while Gareth Bale joined Ronaldo in the final third.
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.
Moments later, Los Blancos had a huge penalty shout when Toni Kroos went down inside the box under a challenge from Juanfran, but the referee waved away the home side's appeals.
Atletico actually had the ball in the back of the Real Madrid net in the 19th minute, but Diego Costa was adjudged to have felled Sergio Ramos in the build-up, before Oblak did well to keep out a Ronaldo strike down the other end.
Oblak then made a really smart stop to keep out a close-range Raphael Varane effort in the 27th minute as Real continued to create opportunities.
Atletico's clearest chance of the first period arrived on the half-hour mark when Costa broke into the Real box, but the Brazilian-born Spain international saw his low strike saved by Los Blancos stopper Keylor Navas.
The home side ended the first period on the front foot, and came close to taking the lead in the 42nd minute when Marcelo curled the ball towards the top corner, but the left-back's effort rattled the woodwork before Oblak kept out a strike from Vazquez moments later.
Vazquez also had the first half-chance of the second period when he met a cross from Marcelo in the 51st minute, but the attacker's header was never threatening to trouble Oblak.
Real Madrid did take the lead in the 53rd minute, however, when Ronaldo expertly volleyed an inch-perfect Bale cross into the corner of the net for his 40th goal of the campaign.
The response from Atletico was strong though, and the visitors levelled the scores just before the hour when Vitolo managed to squeeze the ball into Griezmann, who finished into the back of the net from inside the box.
Navas then had to keep out a strike from Koke as the visitors looked to complete the turnaround at the Bernabeu.
Ronaldo was surprisingly replaced by Karim Benzema in the 63rd minute of the match, while Atletico boss Diego Simeone also made alterations during the same period as Gabi and Angel Correa were introduced, with Costa among those leaving the field.
Saul Niguez curled a low effort wide of the Real Madrid post 20 minutes from time, before Bale headed a Dani Carvajal cross wide of the post down the other end as the match headed for its final 10 minutes at 1-1.
Atletico had a huge chance to score a second in the 82nd minute when Griezmann delivered a low cross towards Correa, but the Argentine, who was unmarked, just could not make contact.
Real Madrid were the team pressing for the game's third goal in the final stages - and Ramos came close late on with a brilliant free kick that was kept out by Oblak - but Atletico held firm to pick up yet another positive result at the Bernabeu as they strengthened their grip on second spot.
REAL MADRID (4-4-2): Navas; Carvajal, Varane, Ramos, Marcelo; Lucas, Kovacic (Modric 72'), Kroos, Asensio (Isco 72'); Ronaldo (Benzema 64'), Bale
ATLETICO MADRID (4-4-2): Oblak; Juanfran, Savic, Godin, Lucas; Vitolo (Correa 61'), Thomas (Gameiro 82'), Saul, Koke; Griezmann, Costa (Gabi 71')