Carlos Vela gave the visitors the lead in the opening minute and, although that was cancelled out by Javier Saviola before the interval, Xabi Prieto scored the decisive goal after 59 minutes.
Defeat leaves Malaga in fifth place, 10 points behind leaders Barcelona.
Basement side Osasuna ended a run of five straight away defeats with an emphatic 3-0 win at fellow strugglers Espanyol.
The visitors took the lead through Alvaro Cejudo midway through the first half.
Kike Sola grabbed another in the 63rd minute before Manuel Omwu added further gloss to the scoreline 12 minutes from time.
Helder Postiga scored twice as Real Zaragoza hit back from two goals down to beat 10-man Deportivo La Coruna 5-3 in a topsy-turvy game at La Romareda.
The visitors had gone into an early 2-0 lead thanks to goals from Bruno Gama and Riki, but Apono brought Zaragoza back into the game from the penalty spot before half-time.
Pizzi was then shown a second yellow card for diving four minutes into the second period, and the hosts made their man advantage pay in spectacular style as Paco Montanes and Alvaro Gonzalez put them 3-2 in front before Postiga bulleted in two headers.
Rodolfo Bodipo got one back for Depor in the last attack of the game but it mattered little.
Rayo Vallecano also produced a second-half comeback to beat 10-man Celta Vigo 3-2.
Iago Aspas had fired the visitors into a two-goal lead in the first half, but the game swung in Rayo's favour five minutes before half-time when defender Gustavo Cabral was shown a second yellow card.
Leo Baptistao and Tito then headed the hosts back on level terms after the break and Piti sealed the comeback with a penalty eight minutes from time.
With a host of injuries and five successive defeats to their name, Real Mallorca feel less than optimistic heading into their match with Barcelona.
The Catalans themselves will be keen to get back on the winning trail after Wednesday's 2-1 reverse at Celtic and pull away at the top of the table.
Mallorca were beaten 1-0 by Deportivo la Coruna last time out and their plight has not been helped by Giovani dos Santos becoming the latest player to join a long list of absentees.
Midfielder Tomas Pina has said the situation has gotten so bad manager Joaquin Caparros has told his players to avoid clashes in training.
Pina told AS: "It is a plague of injuries that greatly changes planning for the season and the development during it, and in our case even more so because we are a small squad.
"Sometimes the coach tells us to be careful because you have to be aware that the situation is uncomfortable and if you can avoid a collision in training, then it's best to do so."
Atletico Madrid may be second in the table ahead of the visit of Getafe on Sunday, but coach Diego Simeone has had to defend Adrian Lopez as the forward has scored just once in 13 matches.
He told Marca: "In principle he gives us the possibility of playing in different areas, he isn't an out and out goalscorer but he offers us offensive variety and he can make goals.
"I don't think he has an obligation to score because every game he is improving and I am happier every time with the development he is having."
Adrian could have a big role to play this weekend when Getafe visit the Vicente Calderon as Diego Costa is still out with a muscular problem but otherwise Simeone has a full squad to choose from.
Current holders Real Madrid have injury concerns ahead of their trip to Levante.
Both recognised centre forwards Gonzalo Higuain and Karim Benzema are ruled out with muscle strains.
Sami Khedira also remains on the sidelines with a thigh injury but there could a return ahead of schedule for Fabio Coentrao after he returned to training on Thursday.
For the home side Obafemi Martins will return to lead the line on Sunday as he was ineligible for their European tie with FC Twente on Thursday and fringe players Dariusz Dudka and Theofanis Gekas are the only injury absentees from Juan Ignacio Martinez's squad.
Sunday's other matches see Real Valladolid host Valencia, while Sevilla travel to Athletic Bilbao.
Friday's La Liga Results
Saturday's La Liga Results
Sunday's La Liga Fixtures