But in form Atletico, who face Leicester City on Wednesday in the Champions League quarter final first leg, battled back as Griezmann slid in to score with five minutes of action to go.
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.
Atletico Madrid president Enrique Cerezo has categorically denied reports that Real Madrid could buy Theo Hernandez, saying "people should be more serious".
Manchester United are known to be long time admirers of Atletico Madrid star Antoine Griezmann whose Old Trafford summer switch would cost José Mourinho € 100 million which is the release clause included in the Frenchman's contract with the Colchoneros.
Saul Niguez glanced an early header past Keylor Navas' far post but it was Oblak who made the first save of the match, getting down low to his right to stop a fierce strike from Ronaldo from the edge of the area.
Oblak was beaten on the half-hour mark but Savic came to Atletico's rescue, the centre-back heading Ronaldo's strike from close range up and over the crossbar from nearly on the goal line.
Flood-like situation in J&K, Jhelum above danger mark in Srinagar
Sonam Lotus, the director of the meteorological department, however, ruled out floods of the magnitude seen in 2014. He also said there is possibility of scattered to widespread rains or thundershowers over the state till April 8.
Atletico, though, remained risky on the counter-attack, as Griezmann made the most of a loose pass from Sergio Ramos and sent a low shot goalwards which Navas pushed behind at full stretch.
Real defender Dani Carvajal then fired his shot over the crossbar, with the Bernabeu faithful in full voice. "Their midfielders, their backs. they all know how to play".
Despite their dominance of possession, Real were hit on the break as the hour mark passed.
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.
- Real Madrid have scored more goals from set-piece situations than any other side in La Liga this season (25).