Atletico sit sixth in the standings on six points, three behind leaders Real Madrid and Betis and one adrift of Barcelona, Villarreal, and Athletic Bilbao.
Griezmann scored the winner in the 66th minute, assisted by fellow substitute Thomas Lemar.
Lemar made a fine individual run from the left touchline and found his France teammate Griezmann on the edge of the area, who lashed in a shot that was deflected off the back of the defender and past the helpless goalkeeper.
With new signing Edinson Cavani sitting in the stands, Valencia were the better side during the first half and thought they had opened the scoring when 19-year-old American midfielder Yunus Musah netted a stunning long-range shot in the 24th minute.
But following a lengthy VAR review, the goal was ruled out due to a foul by Mouctar Diakhaby on Joao Felix in the build-up.
Just before halftime, Thierry Correia was initially shown a straight red card for a foul on Atletico's Alvaro Morata.
But referee Guillermo Cuadra switched it to a yellow after checking the VAR footage.
"What I don't like is the lack of criteria. We never know when the referees will or will not use the VAR and that's really frustrating," frustrated Valencia manager Gennaro Gattuso told Movistar Plus.
After the break, Simeone brought on Griezmann and Lemar and Atletico took charge of the game.
"We didn’t have the game under control but we had many chances to score, three clear opportunities that were denied by their goalkeeper, who was instrumental to hold us to only one goal," Simeone told Movistar Plus.
"We struggled get into rhythm, but Lemar and Griezmann came in and gave us more tranquility to impose our gameplan late in the match".
Atletico will face Real Sociedad away on Saturday, while Valencia will host Getafe on Sunday.