Malaga were without the services of Brazilian striker Charles through suspension, which opened up a spot in the team for Spanish attacker Keko. Sandro Ramirez and Pablo Fornals both kept their spots in the final third, but there was a change at left-back as Miguel Torres replaced Juan Carlos, who moved into midfield.
As for Atletico, Yannick Ferreira Carrasco missed out through suspension, while Nico Gaitan, Kevin Gameiro, Tiago and Sime Vrsaljko all remained on the sidelines. Diego Godin was not risked after returning late from international duty, meanwhile, meaning that Lucas Hernandez started alongside Stefan Savic at centre-back.
It was Atletico that had the game's first attempt on target in the sixth minute of action, but Koke's effort from distance was fairly comfortable for Carlos Kameni, who got down low to make the save.
Malaga's first sight of goal arrived in the 12th minute when Ignacio Camacho rose highest inside the Atletico box to meet a long throw, but the midfielder's header was always wide of Jan Oblak's post.
It was the home side that were enjoying more of the ball as the first period developed, but Atletico were the more threatening, and Simeone's side made the breakthrough in the 26th minute when Koke slid the ball past the onrushing Kameni after smart work from Fernando Torres.
Malaga again enjoyed some decent possession after falling behind, but aside from Sandro, the home side lacked invention in the final third as Atletico shut up shop at the back.
A spectacular flick from Keko saw Malaga register their first shot on target in the final moments of the first half, but Oblak was on hand to make the save as the visitors led at the interval.
Angel Correa was introduced in place of Thomas Partey in the 53rd minute as Atletico looked to kill the match with a second goal, although not too much was harming them down the other end as Malaga continued to struggle.
Indeed, the match reached the hour mark with Atletico still extremely comfortable in their defensive shape, with Sandro the only player in a blue and white shirt looking capable of undoing the centre-back pairing of Savic and Hernandez.
Juan Carlos tried his luck from a volley 20 minutes from time as Malaga forced the issue with a couple of corners in quick succession, but the left-back's effort went into orbit, before Griezmann missed the post with a low effort down the other end.
Atletico doubled their lead in the 74th minute, however, when a super flick from Fernando Torres found Luis, and the Brazilian left-back chipped the onrushing Kameni for his first goal of the season.
Sandro tested Oblak with a long-range strike 10 minutes from time as Malaga looked to hit back, before Diego Llorente sent a close-range header wide of the post as Atletico survived a couple of dangerous moments in quick succession.
Godin was introduced in place of Griezmann as Atletico closed out the game in the final moments, however, to move above Sevilla into third and just five points behind second-placed Barcelona.
Next up for Atletico is a home game against Real Sociedad on Tuesday night, while Malaga's search for a win will continue when they travel to Sporting Gijon one day later.