Top scorer Griezmann latched onto a through ball from Koke to arrow a first-time finish into the bottom corner in the 10th minute, while Gameiro notched his 10th league goal this season three minutes after the break with the help of a deflection.
Griezmann then rounded off the scoring in the 83rd when he pounced on an over-hit pass from team mate Thomas Partey and poked home to score his 12th league goal of the campaign.
It was a crucial victory for Atletico, who lost to Barcelona last weekend and suffered a disappointing 1-1 draw at Deportivo La Coruna on Thursday.
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Club favourite Fernando Torres sat in the stands after recovering from head trauma sustained against Deportivo and was given a standing ovation by supporters in the second half.
Atletico are fourth place in the La Liga standings on 49 points, one ahead of Real Sociedad, who won 3-2 at Real Betis on Friday.
(Reporting by Richard Martin; Editing by Toby Davis)
