Tiago, Antoine Griezmann an Diego Godin were all on target at the Vicente Calderon as Atletico stayed within four points of city rivals and league leaders Real Madrid in a match that saw both teams reduced to 10 men late on.
Malaga had won five league games in succession heading into Saturday's clash but they were second-best in the first half as Atletico took a 2-0 lead into the interval.
Tiago headed the home side into a 16th-minute lead from Koke's corner and Atletico exploited Malaga on the counter-attack, with Griezmann the beneficiary three minutes before half-time.
Roque Santa Cruz reduced the deficit in the 64th minute, but Atletico centre-back Diego Godin sealed the points seven minutes from the end.
Atletico captain Gabi was sent off for a second bookable offence with two minutes remaining, following Samu's dismissal 15 minutes earlier.
"They played very well. I think the team performed very seriously," Simeone told reporters.
"We understood very well that we had to erode Malaga's defence as they were playing very well.
"We closed up very well so our opponent couldn't attack us. Then we managed to counter-attack. We applied a very high pressure.
"The ball circulated fluidly and we played a very complete match."
Atletico's three-goal haul continued their purple patch on home soil, having defeated Cordoba 4-2 last time out at Vicente Calderon on November 1.
The Madrid club have scored 13 goals from their past four home fixtures in Liga.
"Scoring three goals is not easy," the Argentinean boss added. "The last game at home we scored four goals and today three.
"The other day we scored one away, another more in Getafe. The most important thing is the team is creating chances.
"Today we created danger in different ways. Firstly from set pieces which is something we do very well, but we have taken chances too.
"For instance, the second goal was a great one."
