La Liga's reigning champions have now drawn two and won three of their opening five games.
Fans and players later celebrated together outside the stadium in Valladolid, with more supporters rejoicing back in Madrid.
Real Madrid will play against Villarreal in their last game of the season, and Zinedine Zidane's side needs to win this match in order to keep their hopes alive of winning the league.
Atletico Madrid have a chance to win La Liga 2020-21 if they win all the three games that are left in the Spanish competition.
Despite the defeat, Atletico Madrid holds the top spot on the La Liga table with 66 points from 29 games.
One victory from their opening four league games left Atletico seven points adrift of Barcelona a fortnight ago but three on the spin have now steered Diego Simeone's side back on track.
Diego Simeone has claimed if Lionel Messi played for Atletico Madrid, his side would have beaten Barcelona on Sunday.
Griezmann turned his back on interest from Manchester United to sign a new contract after Atletico lost an appeal against a transfer ban.
Atletico Madrid has fallen to Real Madrid in the quarters, semis and twice in the final in the past four seasons.