Koke, the scorer of the winner in Atletico's last win at Malaga in 2014, capitalised on some excellent hold-up play from Fernando Torres to nudge Atletico ahead in the 26th minute of a scrappy game.
Filipe Luis then scooped up a loose ball in the 74th minute following another run from Torres to dink his finish over Carlos Kameni for his first goal of the season.
Malaga's Rosaleda stadium holds special memories for Atletico manager Diego Simeone as it was the scene of his first game in charge of the club back in January 2012, although his side had won only one of their five previous matches there.
They looked to be in for another difficult game after Nico Gaitan and Kevin Gameiro sustained injuries in midweek to join the suspended Yannick Carrasco as well as Augusto Fernandez, Tiago, Sime Vrsaljko and Miguel Angel Moya on the sidelines, meaning Simeone had to call on two reserve players to complete his 18-man squad.
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Malaga, however, have had a rotten season, changing their manager twice, and had won just one of their previous 15 league games heading into the fixture, and Michel's side offered little resistance.
"What pleased me the most was the bravery and defiance we showed against the difficulties we faced," Atletico coach Simeone told reporters.
"We came here with two youth players and the team played just as well as we always do, and that says a lot about us and the hard work we always put in."
Atletico are provisionally third in the standings on 58 points after climbing above Sevilla, who host Sporting Gijon on Sunday. Leaders Real Madrid, who have 65 points, entertain Alaves on Sunday, while champions Barcelona, two points behind, visit Granada.
Also on Saturday, Real Sociedad's hopes of finishing fourth faded further after they drew 1-1 at home to Leganes, extending their winless run to three games.
Leganes went ahead in the 29th minute on a rain-swept afternoon in San Sebastian when Alexander Szymanowski pounced on a moment of indecision from goalkeeper Geronimo Rulli to latch on to a through ball and lob his Argentine compatriot.
Juanmi Jimenez levelled for Real Sociedad eight minutes into the second half, smashing in a cutback from youngster Alvaro Odriozola.
The Basques tried to build on their momentum, but they were unable to convert the few chances they managed to create.
Eusebio Sacristan's side are fifth in the standings on 49 points, eight behind fourth-placed Sevilla, who have a game in hand, and nine adrift of third-placed Atletico.
Athletic Bilbao, in seventh, beat basement club Osasuna 2-1 to move to within one point of sixth place Villarreal after Fran Escriba's side were beaten 3-2 at home to Eibar, who are eighth, three points behind Athletic.
Espanyol are ninth in the standings, one point back from Eibar, after leaving it late to beat Real Betis 2-1 on Friday, Javi Fuego hitting the equaliser in the 88th minute and then veteran Jose Antonio Reyes providing the winner in the 90th.
(Reporting by Richard Martin; Editing by Toby Davis, Neville Dalton)
