That goal came on 11 minutes to level the scores at 1-1 after Celta had taken an early lead through a Gustavo Cabral header.
"It was a vibrant game, emotional, with many errors, but two teams going for the win".
But Yannick Carrasco drew the home side level with a stunning volley in the 86th minute and France global Griezmann completed the comeback by sidefooting Kevin Gameiro's flicked header in at the near post in the 89th.
Celta also hit the post before the break through Jozabed in an entertaining end-to-end encounter played in torrential Madrid rain.
After controlling the ball inside the penalty area with his back to goal, he pulled off a sensational overhead strike to loop the ball over the keeper and into the back of the net - vintage Torres.
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However, it was not a ideal night for the Spaniard as he failed to take advantage when Carrasco was felled by Facundo Roncaglia inside the penalty area.
Victory takes Atletico a point clear of Real Sociedad as all of the top five in La Liga won this weekend.
Jorge Sampaoli's side, who are three points off the top, had lost ground on leaders Real Madrid and second-placed Barcelona after collecting one point from their previous two matches. However, for all Las Palmas' pretty football, they were caught out by one simple long ball as Iborra flicked on Rico's goal kick and Correa raced through to finish. There was a moment when we looked far from getting back into it.
"Sergio made a couple of incredible saves and it was a very hard game, but I feel satisfied that the team could stand up and be counted in an important game".