The visitors were made to sweat for the victory and had endured a frustrating afternoon at La Rosaleda until the Spain international popped up with the winner on 70 minutes.
Not for the first time this season away from the Calderon, Atleti struggled to create many chances but Simeone has instilled a winning mentality in the team and once again they did just enough to take all the points home with them.
The Madrid side have now gained 49 points, three more than Barcelona, who entertain Elche on Sunday.
Atletico were without their captain Gabi and attacking midfielder Raul Garcia, who were both suspended, so Simeone gave a rare start to 19-year-old Oliver Torres, and paired Koke with Tiago in the centre of midfield.
Bernd Schuster meanwhile opted for a five-man defence, which will do little to dispel the criticism he has received for being too cautious.
The visitors had an uncomfortable start to the game but soon took control of possession and began creating chances, with Willy Caballero saving from Juanfran and then coming to gather a gather an inviting cross from Koke.
But it was Malaga that created the better chances, Eliseu forcing a save from Thibaut Courtois and then Samuel shot inches past the far post from the edge of the area, while Filipe Luis nearly diverted the ball into his own net.
Torres was replaced by Adrian Lopez at the start of the second half, and the substitute squandered a fine chance to score within 15 minutes of coming on, taking one touch too many when he was clean through on goal, and defender Weligton was able to recover and rob him of the ball.
It had been Atleti's best chance of the match and their frustration was beginning to tell when Arda Turan smashed a hopeful long-range effort well over the bar.
With a goal looking less and less likely, Koke came to the rescue with 20 minutes remaining, although Costa, as ever, was heavily involved.
The Brazilian squared the ball from the left hand side of the box to Adrian, who forced a save from Caballero and the loose ball fell into the path of the midfielder, who lashed it into the empty net.
From then on Atleti just wanted to hold on to their lead, and Simeone withdrew David Villa, who produced another unconvincing performance, for centre-back Toby Alderweireld.
Sergio Sanchez came close to converting a corner towards the end but the Atleti backline stood firm.
The only bad news for Los Rojiblancos is that Juanfran picked up a booking and will be suspended for next week's top-of-the-table clash with Barcelona.