The reigning Liga champions never really hit top gear at the Vicente Calderon and, despite looking comfortable in the first period, Diego Simeone's men were made to fight for all three points.
Malaga travelled to the capital on the back of five successive league wins, but Javi Gracia's side struggled throughout the first half, with Tiago heading Atletico ahead before Antoine Griezmann doubled his team's lead in the 42nd minute.
Roque Santa Cruz pulled one back for Malaga with 26 minutes to go as the away side appeared far more decisive and fluid in the final third after half-time.
Raul Jimenez, a second-half substitute for Mario Mandzukic, saw a couple of excellent chances go begging, although Atletico ultimately sealed all three points seven minutes from time as Diego Godin nodded in the third from close range.
Although Malaga came into the clash in fine form, Atletico looked very much in charge during the early exchanges as they pressed high and pushed the visitors back.
Koke appeared destined to give the hosts a 12th-minute lead as he latched on to Juanfran's cut-back and fired at goal following Mandzukic's step-over, only for Weligton to make a crucial block.
Atletico were not to be denied from the resulting corner, though, as Tiago met Koke's corner and headed beyond Carlos Kameni, who probably should have done better.
Simeone's men appeared to relax after taking the lead, inviting Malaga back into the contest as the away side began to enjoy more possession.
But, even with a hamstring injury keeping the ever-reliable Miranda out of Atletico's defence, Malaga were unable to break through the hosts' backline and test Miguel Angel Moya in goal.
As a result, Atletico punished Malaga on the counterattack just before the break to open up a two-goal cushion.
Arda Turan raced down the right after linking well with Mandzukic and his teasing low cross was tapped in at the back post by the lurking Griezmann.
Malaga began the second half with renewed determination and they went close to pulling one back in the 49th minute, but Juanmi failed to hit the target after pouncing on Santa Cruz's flick-on.
Much-improved Malaga finally brought themselves within touching distance of Atletico three minutes later, as Santa Cruz, starting because of an injury to Nordin Amrabat, steered in Samu Castillejo's deep cross from a tight angle.
The visitors continued to push for an equaliser, but were ultimately undone again at the back as Tiago lifted a cross over Kameni and Godin bundled over the line to complete a hard-fought Atletico victory.
