A fourth win in five games in all competitions moved Atletico Madrid men up to third in LaLiga, one point behind second-placed Barcelona and a further point back from leaders Real Madrid.
Gaizka Garitano’s men never seriously threatened to secure what would have been their first victory since the opening day of the league campaign, even before Fajr’s premature departure and they remain precariously positioned just one point above the relegation places.
A sluggish, disjointed opening to the game was notable only for Simeone being forced to introduce Gabi from the bench after just 19 minutes.
The club skipper had been named among the substitutes, presumably in a bid to keep him fresh for the Bayern Munich game, but he was forced into the fray after Fernandez was stretchered off.
Having taken a while to settle, Atletico went close to breaking the deadlock on 21 minutes when Angel Correa split the Deportivo defence with a clever throughball, but Griezmann dragged his low shot narrowly wide of the post.
The home side duly upped the tempo in the wake of that missed chance, creating another moments later as Nicolas Gaitan’s goalbound effort was blocked by a cluster of Deportivo defenders.
Atletico remained on the front foot as half-time approached despite losing a second player to injury as Gimenez was forced off with a thigh problem.
And they received an unexpected boost in stoppage time when Fajr picked up his second yellow card of the afternoon for a ludicrous challenge on Gaitan.
Griezmann had an effort correctly ruled out for offside two minutes into the second half, Gabi then fired wide and Yannick Carrasco was denied twice in quick succession by Deportivo goalkeeper German Lux as the home side piled on the pressure.
But despite Lux’s heroics and some resolute defending, the 10 men were eventually undone on 70 minutes as Griezmann converted from Gameiro’s right-wing cross.
Atletico were largely untroubled in the final quarter with the notable exception of a last-minute strike from Emre Colak, which was headed clear by Diego Godin, as Simeone’s men avoided the last-gasp headaches that neighbours Real Madrid had suffered on Saturday in drawing to Las Palmas.