Antoine Griezmann and Joao Felix missed the best openings of a cagey first half, before visiting captain Koke finished neatly into the bottom-right corner in the 49th minute.
Jan Oblak made a fine left-handed save to preserve the lead, and Atleti held on despite Angel Correa's late red card, earning a fifth successive league win and boosting hopes of a top-four finish.
Griezmann's early volley forced Stole Dimitrievski into a reaction stop at his near post, before Joao Felix poked agonisingly wide after meeting Rodrigo de Paul's free-kick at the back post.
Joao Felix then sent a disappointing header over the bar from a right-wing corner on 34 minutes, but the fleet-of-foot Portugal international was Atleti's brightest attacker in a competitive first half.
Stefan Savic headed over from another set-piece at the end of a first half in which chances came at a premium, with both sides each registering just one shot on target each before the break.
Atleti went up a gear at the start of the second half, however, with Koke exchanging a neat give-and-go with Joao Felix before bending the ball into the bottom-right corner.
Mario Suarez drew a stunning save from Oblak on the hour and substitute Correa put his team in a difficult spot when he saw red on 85 minutes for shoving Alejandro Catena, but the visitors clung on.