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.
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 in La Liga on 49 points, one ahead of Real Sociedad, who won 3-2 at Real Betis on Friday.
It was Simeone's 200th league game in charge of Atletico, having taken over in December 2011 with the team in freefall and teetering above the relegation zone. He is the second Atletico coach to reach the landmark, trailing the late Luis Aragones, who coached the club in 407 league encounters.
The Argentine has utterly transformed their fortunes over the last five years, securing top-three finishes four years in a row and leading the team to their first league title in 18 years in 2014 as well as reaching two Champions League finals.
Deportivo continued their improvement under new coach Pepe Mel as they picked up their first league win of 2017 on Sunday by beating fellow strugglers Sporting Gijon 1-0 away from home to move four points clear of the relegation zone.
Mel's first game in charge was Thursday's 1-1 draw with Atletico, which halted a four-game losing streak under his sacked predecessor Gaizka Garitano.
Former Real Madrid forward Jese scored twice as Las Palmas won their first game in six league outings by thrashing basement club Osasuna 5-2. Jese found the net for the first time since joining his hometown club on loan from Paris St Germain at the end of January.
Gijon 0 Deportivo 1
(Griezmann 10, 83, Gameiro 48) Valencia 0
Las Palmas 5
(Jese 7, 87, Livaja 55, Garcia 70-og, Mesa 76) Osasuna 2
(Kodro 31, 37)
(Garcia 72-P) Malaga 0
P W D L GD Pts
26 18 6 2 55 60
25 18 5 2 41 59
25 17 4 4 20 55
26 14 7 5 26 49
26 15 3 8 6 48
26 12 9 5 19 45