France international Griezmann scored his fifth goal of the season from close range 20 minutes from fulltime after the visitors were reduced to 10 men following midfielder Faycal Fajr's sending off on the stroke of halftime.
The result put Atletico third on 12 points from six games, two behind leaders Real Madrid who were held to a 2-2 draw at Las Palmas on Saturday.
With Wednesday's home game against Bayern Munich looming, however, Atletico midfielder Augusto Fernandez left the pitch on a stretcher with a suspected knee injury before defender Jose Gimenez limped off with a groin problem.
After last Wednesday's 1-1 draw against Barcelona at the Nou Camp, Atletico rested Stefan Savic and Saul Niguez while Gabi and Kevin Gameiro started on the bench.
The hosts got off to a low-key start but gained the upper hand when Deportivo's Fajr was sent off a minute into first-half stoppage time after a charge on Nicolas Gaitan earned him a second booking.
After Griezmann had an effort ruled out for offside, Yannick Carrasco came close eight minutes into the second half but his superb curling shot from the edge of the box was tipped onto the bar by Deportivo keeper German Lux.
The breakthrough eventually came when Gameiro collected a superb through ball from Juanfran in the box and Griezmann tapped in from his compatriot's cross to give Atletico a deserved victory.
(Writing by Julien Pretot; Editing by Toby Davis)
