However, the lead lasted only four minutes as Griezmann struck back for the visitors, dispatching a finish confidently into the net from close range.
Striker Karim Benzema also started from the bench, replacing Ronaldo in the 64th.
Griezmann indicated last month that he would decide on a move before the World Cup finals in Russian Federation, which start on June 14.
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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. Ronaldo appeared unhappy as he made his way to the dugout. Ronaldo's goal against Atletico was his 20th in his last 10 games in all competitions.
Real are next in action on Wednesday night when they face Juventus in the second leg of their Champions League quarter-final. However, Real have a healthy lead in the tie, making it something of a unusual move by the Real Madrid boss. The former Chelsea forward was released clean through on goal by a deft flick from Koke but his low shot at the near post was brilliantly stopped by Keylor Navas.
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The Atletico star is clearly a fan of the video game Fortnite and has already given us a few celebrations inspired by the game.
Barca now hold an 11 point lead over Atletico but Diego Simeone's side can still lift a trophy at the end of the term via the Europa League, with Los Rojiblancos well placed to reach the semi finals after beating Sporting CP 2-0 on Thursday.
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A win for Real would have ended Atleti's slim hopes of claiming the title and that looked likely as Cristiano Ronaldo finally broke the deadlock with a fine finish after 53 minutes, slotting home an excellent Gareth Bale cross from the left.