La Liga Wrap: Atletico start 2014 with victory
On a frustrating night for Diego Simeone's side, they had to wait until the 70th minute before they could get the breakthrough from Koke.
Malaga were quite happy to sit back, allowing the visitors to have possession and hit them on the counter attack - but Atletico's pressure eventually told with the 21-year-old midfielder's third league goal of the season.
The win moves Atletico three points clear at the top of the league, with Barcelona able to retake top spot if they beat Elche on Sunday.
Valencia returned to winning ways against local rivals Levante as they recorded a 2-0 victory in Juan Antonio Pizzi's first game in charge.
Sofiane Feghouli missed chances in the opening minutes but Pablo Piatti made no mistake in the 42nd minute with the game's opening goal.
Feghouli and Helder Postiga wasted chances to double their lead in the second half, but Feghouli finally found the back of the next in the 73rd minute to seal their first win in three matches with his first goal of the season.
Real Betis missed the chance to close the gap at the bottom of the table as they were held to a 0-0 draw by Real Valladolid.
The draw means Juan Garrido's side have not won in their past 11 league matches and are five points from safety having played a game more than their rivals.
Elsewhere, Almeria recorded back-to-back wins for only the second time this season with a 3-0 victory over Granada.
A 14th minute strike from Sebastian Dubarbier and a Verza penalty just before the half hour put Almeria 2-0 ahead at the break, and Aleix Vidal secured the win with a third with 11 minutes to play as Francisco's side move three places up the table.