Although captain Sergio Ramos twice went close in stoppage time, Madrid were unable to force a victor and remain third - four points behind their neighbours in LaLiga.
Griezmann equalized less than five minutes later with a strike from near the penalty spot after a move started by Vitolo inside the area.
The home side were aggrieved not to be awarded a penalty after Toni Kroos went down under Juanfran's clumsy challenge two minutes later, and the Germany worldwide let his frustration show when he was booked for a needless foul on Griezmann.
That it was still scoreless at half-time was mostly due to goalkeepers Jan Oblak and Keylor Navas, though the woodwork also played a role with the home team's Marcelo and Marco Asensio hitting the crossbar.
Oblak then made a really smart stop to keep out a close-range Raphael Varane effort in the 27th minute as Real Madrid continued to create opportunities.
"Errors will have to be reduced by the team and since we know how they play, we just have to go for the victory this weekend".
Zinedine Zidane's men set out in the 219th Madrid derby in determined fashion and might have taken a ninth-minute lead had Ronaldo managed to make better contact with Gareth Bale's flick-on at the far post.
Real were nearly paid to rue their missed opportunities when Koke sent Diego Costa through on goal, but the ex-Chelsea star's near-post attempt was tipped wide by Keylor Navas. Bale nearly had it but put a hard header wide, while Sergio Ramos nodded past from a corner and saw his curling free-kick tipped over by Oblak. But it still required a well-controlled finish by Ronaldo, who guided a 12-yard volley beyond Atletico's impressive shot-stopper to find the net for a 10th consecutive game.