With Barcelona not re-starting their season until Sunday after the Christmas interlude, Atletico took advantage to move three points clear of Barca.
Atletico lacked a cutting edge against a well-marshalled Malaga defence with the league's top scorer Diego Costa having a subdued match in a misfiring attack.
Koke finally made the breakthrough, slotting the ball home after Willy Caballeros saved from Adrian Lopez.
"Malaga were happy for us to have the ball and play on the counter-attack. They were strong at the back," Atletico coach Diego Simeone told a news conference.
"We were finding it difficult to create openings but in the end we managed it through a team effort.
"We continue to go match by match and expect Barcelona to win tomorrow and go back to the top."
Atletico now have 49 points from 18 games although Barcelona will return to the top with victory at home against Elche.
Real Madrid, who are eight points adrift, face Celta Vigo on Monday.
Malaga played five men in defence and the tactic succeeded in stifling Atletico's attacking thrust with Costa and David Villa struggling to get into the game and youngster Oliver Torres, given a chance on the left, failing to unsettle Malaga.
Lopez and Cristian Rodriguez were both brought on to add pace to the Atletico attack and with the match starting to open up, Koke struck.
Lopez's close range shot was blocked by Caballeros and Koke put the ball into an open goal.