An outstanding save by Malaga goalkeeper Willy Caballero denied Atletico the opportunity to wrap up the title at their Vicente Calderon stadium.
The Argentinian produced a fingertip save to keep out a curling shot from Adrian in the final minute of stoppage time, ensuring the game ended 1-1.
It sets up a mouthwatering showdown between Atletico and their nearest title rivals Barca next weekend, with Diego Simeone's side only requiring a point to lift their first league title in 18 years.
But Atletico will feel distraught at letting the chance to seal the title once and for all slip through their fingers.
Atletico created the better of the chances but fell behind to a shock goal by Samuel Garcia midway through the second half, as a result of a terrible mix-up between their usually reliable defence and goalkeeper Thibaut Courtois.
A header by Toby Alderweireld nine minutes later levelled things up and set up an enthralling finale, with Malaga finishing the game with 10 men as Marcos Angeleri was sent off in the final few minutes.
Barcelona played their part in setting up a winner-takes-all clash after they drew 0-0 against strugglers Elche.
The results mean Barca and Atletico will face each other at the Nou Camp in a title showdown next week, with only a win enough for Gerardo Martino's side to claim the league honours.
Atletico lead Barca by three points following the two draws on Sunday but victory for Barca would give them their 23rd Liga crown on head-to-head record, having drawn with Atleti earlier in the season.
Celta Vigo ended any lingering hopes Real Madrid had of league glory by claiming a 2-0 victory over Carlo Ancelotti's men at Estadio Balaidos.
Celta claimed their third win on the bounce after Brazilian forward Charles' capitalised on two errors from Real to bag a brace and leave the visitors five points behind leaders Atletico with just one match remaining.
At the other end of the table, Almeria gave themselves a great chance of avoiding relegation with a 2-0 victory over fellow strugglers Granada.
Almeria had climbed out of the bottom three with two straight wins and made it three thanks to penalties from Verza and Aleix Vidal.
That lifted them three points above the relegation zone with only one game remaining and a point ahead of Granada, who had Jeison Murillo sent off.
Getafe took advantage of a weakened Sevilla side to claim a vital victory in their fight against relegation. Sergio Escudero's 70th-minute goal gave them a 1-0 victory to help them climb three points clear of the bottom three with one match to play.
Real Sociedad striker Imanol Agirretxe struck late to ensure the Basque Country derby ended 1-1, spoiling Athletic Bilbao's celebrations following their qualification for the Champions League.
Iker Muniain's goal from 25 yards gave the hosts the lead to create a party atmosphere at San Mames Barria, but Agirretxe denied Athletic what would have been their first derby win for two years by scoring on 75 minutes.
Espanyol drew 1-1 with relegation battlers Osasuna, when Diego Colotto's opener was cancelled out by Javier Acuna Caballero before the half-time whistle.
Meanwhile, already demoted Real Betis defeated second bottom Real Valladolid 4-3 thanks to Juanfran's stoppage time winner.
Javi Guerra put Valladolid ahead in the first minute before Carlos Pena's own goal levelled the scores. Pena atoned with a goal at the right end after the break but Betis equalised through Jorge Molina in the 54th.
The momentum swung back to Osasuna five minutes later when Javi Guerra scored from the penalty spot, but a third equaliser from Ruben Castro in the 76th minute and Juanfran's added time winner wrapped up a rare win for Betis.