Griezmann used his left foot to drive home a perfectly placed throughball by substitute Angel Correa to equalize at the Santiago Bernabeu in the 85th minute.
Pepe put Real ahead in the 52nd, when he shook off his marker and headed Toni Kroos' free kick just inside the far upright.
But Real failed to press for another goal and Griezmann capitalized on its complacency.
Here are five things we learned from the entertaining draw...
Simeone's patience pays off
Having won his last LaLiga trip across the capital, it looked as if Atletico boss Diego Simeone was set to leave the Bernabeu empty-handed this year following Pepe's looping header from a free-kick early in the second half.
However, rather than just accepting defeat and looking ahead to next week's Champions League showdown with Leicester, Simeone opted to freshen things up by sending on Angel Correa before rejigging his team again with the introduction of Thomas.
It proved a shrewd move as Correa set up Griezmann with just five minutes to go and left Simeone leaving no-one in any doubt as to what the result meant with jubilant celebrations at the full-time whistle.
Even Ronaldo can have an off day
Just like Gareth Bale, Karim Benzema and Toni Kroos, Cristiano Ronaldo had been rested for the midweek win at Leganes. The Portugal forward, though, failed to make a telling impact as his first-half effort was headed off the line.
Ronaldo also set up Benzema with a cushioned header, but otherwise was not able to help open up the determined Atletico backline.
Oblak is one of the finest goalkeepers in the world
The 24-year-old Slovenian may not have been able to get anywhere near Pepe's looping header which opened the scoring early in the second half, but without the acrobatics of Jan Oblak, Real would have been home and dry before Atletico's late comeback.
Oblak twice denied Benzema with brilliant point-blank reaction blocks and provided a robust last line of defence whenever Real threatened in the final third.
You cannot give Greizmann an inch
Real had been warned during the first half when Griezmann forced a fine diving save from Keylor Navas, who also beat away an acrobatic effort from the Frenchman during the closing stages.
However, when Correa slipped a pass inside the defenders at the left side of the penalty area for Griezmann to take in his stride, there was only going to be one outcome. It could breathe fresh life into Barcelona's title hopes.
The knives may be sharpening for Zizou
Having now come through some 300 matches with Los Blancos as player and head coach, Zinedine Zidane knows second best is not good enough.
While the destiny of LaLiga remains very much in Real's own hands, they have little margin for error to hold off the expected late charge from Barcelona.
Even though Zidane could yet guide the Spaniards to a second successive Champions League title, lose out to their bitter rivals at home and serious questions will start to be asked as to the direction of his team.