Pepe opened the scoring for Real with a looping header in the 52nd minute and it looked like the hosts would earn the victory that would have moved them five clear of Barcelona at the top of La Liga.
Pepe gave Zidane some cause for concern 23 minutes from time when he was forced off following a collision with Kroos on the edge of the area, while Simeone threw on Angel Correa in an effort to breathe life into Atleti's attack.
Barcelona's setback in Malaga meant Real increased its lead to three points despite the disappointing finish to the Spanish capital derby. Real also has a game in hand, but faces matches against Barcelona and fourth-place Sevilla over the final two months.
Griezmann's goal last February extended Atletico's winning streak at Real Madrid's stadium in league play to three consecutive seasons.
Atleti had offered little by way of a serious threat to the Madrid goal but they found an equaliser in the closing stages, with Griezmann slotting home his 15th league goal of the season.
Real defender Dani Carvajal then fired his shot over the crossbar, with the Bernabeu faithful in full voice.
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"That was a great match by Madrid", Griezmann said about their first league showdown this season.
Griezmann had been starved of service but his best chance of the first half came from a poor Sergio Ramos pass, the forward driving towards goal after picking up the loose ball before testing Navas with a low strike from 25 yards out. It travels to Bayern Munich for its European quarterfinal on Wednesday, and will likely do so without Pepe, who fractured two ribs and had to be substituted after his goal.
"You can't wonder how to stop him", Zidane said about Griezmann.
In line with their "Galacticos" transfer strategy, it appears as though the Spanish giants are ready to make some significant moves in the market despite already possessing the likes of Cristiano Ronaldo, Gareth Bale and Karim Benzema.
Sevilla honoured sports director Ramon "Monchi" Rodriguez, who is leaving the club this summer, with a tribute before the match.
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