Diego Simeone's side would have won the Primera Division title had they beaten the Andalusians at the Vicente Calderon, but know that a draw at Camp Nou next Sunday will be enough
Leaders Atletico were not the only side held, with second-placed Barcelona playing out at a goalless stalemate at Elche.
Real Madrid's 2-0 defeat at Celta Vigo means that Atletico and Barcelona are the only sides who can win the title, setting up a mouth-watering final-day clash between the sides at Camp Nou next weekend.
Atletico know that a point at Barcelona would secure them their first La Liga crown since 1996, but defeat would hand Gerardo Martino's side the title in dramatic circumstances.
David Villa – replacing the injured Diego Costa (thigh) – came closest to scoring in the first half, hitting the bar when one-on-one with Malaga goalkeeper Willy Caballero.
Atletico dominated the first hour, but were made to pay for their profligacy when Samuel Garcia gave Malaga a shock lead in the 65th minute.
Toby Alderweireld failed to deal with a long ball and as a result, Samu got in and behind the defence, lobbing the on-rushing Thibaut Courtois before heading in from an angle.
Alderweireld went from zero to hero when he headed in a 74th-minute corner, but Atletico had to settle for a point, even if Malaga defender Marcos Angeleri was sent off in the dying stages, with Adrian Lopez sensationally denied by Caballero in stoppage time.
The share of the spoils secures Malaga's top-flight status, while Atletico will go into their title showdown with defending champions Barca hoping they do not rue two dropped points.
Costa was not Atletico's only absentee, with suspended defender Diego Godin replaced by Alderweireld, but the Belgium international had little to do in the first half as the hosts dominated without scoring.
Diego Simeone's side first went close in the fifth minute, when Tiago's stabbed effort went out for a corner via the arm of Eliseu.
Atletico's penalty appeals were waved away, and in truth Malaga would have been unlucky if referee Jose Teixeira pointed to the spot, given the close proximity of the defender to Tiago.
Villa's chance followed, but he could only hit the crossbar after being sent through by Raul Garcia's flick-on.
And the hosts headed into the break frustrated after they failed to convert two excellent Juanfran crosses.
The initial chance was poked wide by Koke, who preferred to use his right foot when it seemed easier to shoot with his left, before Garcia nodded a free header wide, although he was distracted by Alderweireld going for the same ball.
Atletico's pressure kept coming after the break, as Koke dragged an effort wide before Villa was kept out by Caballero from a tight angle.
With the hosts pouring numbers forward, they were vulnerable to counter-attacks, and Simeone had Courtois to thank for his excellent save to deny Roque Santa Cruz on the hour mark.
The one-on-one chance served as a warning for Atletico, and it was one they did not heed, as Samu kept his composure to nod in the opener after lifting over Courtois.
Diego had a shot pushed wide with 18 minutes left and less than 60 seconds later, Villa was denied by Caballero after a well-worked set-piece.
Atletico's pressure eventually told, though, as Alderweireld made amends by rising highest to head a corner past Caballero and in.
The hosts could not find a winner despite Angeleri's second yellow card with three minutes left, meaning the stakes could not be higher for their trip to Barcelona.