It was a first win of the current La Liga season after they were held by promoted Alaves and Leganes in their opening two league games.
The Champions League runner-up were outplayed for the first-half in Vigo on Saturday too, as Josep Sense and Theo Bongonda missed great chances.
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But Atletico's luck turned when Koke met Griezmann's fine cross eight minutes into the second-half to give the visitors the lead before Euro 2016's top scorer Griezmann headed home his first two goals of the season in the final 20 minutes, whereas Angel Correa added a fourth two minutes from time.
Celta who once again paid for their chances in promising first-half performance, and paid the price in the end as they are yet to pick up their first points of the season.
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In an uncharacteristic outburst couple of weeks ago, Griezmann claimed Atletico would be "fighting against relegation" rather than challenging Barca and Madrid for the title if they continued to play like in their opening two games after a 0-0 stalemate at Leganes.
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