Croatian forward Nikola Kalinic scored for the second league game in a row to put Atletico ahead in the 26th minute, sliding to the ground to produce a powerful finish after latching on to a wonderful pass from Griezmann.
The Frenchman doubled Atletico's lead on the stroke of halftime by hammering a penalty into the top corner after it was awarded with the help of the Video Assistant Referee but Valladolid came out fighting in the second half.
Fernando Calero headed the home side back into the game from a corner in the 57th and six minutes later they levelled with an own goal from Atletico's Saul Niguez following another corner.
Griezmann had the final say with 10 minutes left, arrowing the ball into the far corner from close range after Valladolid failed to clear. It gave Diego Simeone's side their first away win in La Liga since beating Getafe 2-0 on Sept. 22.
The victory takes Atletico second in the standings, locked on 31 points with leaders Barcelona, who face Levante on Sunday, and three ahead of Sevilla before their game at home to Girona.
"We showed real strength to lift ourselves up again in a game that any other team would have lost," Atletico coach Simeone said.
"I'm very happy; we needed to win away from home again, we are short of players and cannot rotate the team but the players put in a tremendous effort."
Atletico have taken more points than any other team in the league at home, turning their new Wanda Metropolitano stadium into a fortress akin to their beloved old Vicente Calderon, but their title bid has been repeatedly held back by their woeful away form.
Before Saturday, Simeone's side had picked up only one victory away from home and had been held to seven draws on the road, including against struggling sides such as Leganes and Villarreal after taking the lead.
Recent history looked set to repeat itself when Saul diverted into his own net, but Atletico showed their renowned fighting spirit to take the lead again.
"We know that to stay in the fight for the title we need to win games away from home, we need to be strong at home and pick up points away, so getting all three today was fundamental," said Atletico defender Diego Godin.
"The team reacted very well, we rebelled and went all out to win the game and find that third goal. In the end we got it and held on."
(Reporting by Richard Martin; Editing by Ken Ferris and Clare Fallon)
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