Diego Simeone's side, chasing a first championship since 1996, could have ended their near-20-year wait with a home win over Malaga as Barcelona were surprisingly held to a goalless draw by Elche.
However, the destination of the trophy will be decided next Sunday after Bernd Schuster's men earned a 1-1 draw.
The season is set up perfectly for neutrals with Barcelona and Atletico, the only sides that can finish top, facing off at Camp Nou. The hosts require victory and visitors need only to avoid defeat.
Atletico were in complete control throughout at the Vicente Calderon, but found themselves a goal behind when Samu bundled into the net after a defensive error.
Toby Alderweireld's headed home a first league goal to earn a point but a host of missed chances, including Adrian Lopez's late strike being tipped over by Willy Caballero, left a feeling of two points dropped rather than one gained.
For Barcelona, the results will bring a sense of relief after they ran into an inspired performance from Elche goalkeeper Manu, who twice denied Lionel Messi and also kept out an Andres Iniesta volley.
Another side who failed to capitalise on Atletico's profligacy were city rivals Real Madrid, who saw their championship hopes extinguished by a 2-0 loss at Celta Vigo.
Carlo Ancelotti's men only had themselves to blame as mistakes from Sergio Ramos and Marcelo gifted Charles a double.
While the draws earned by Elche and Malaga will be remembered for their impact at the top, they also guaranteed both sides' Liga status for another year.
However, there are several teams currently not enjoying the luxury of such stability with Real Valladolid, Osasuna, Granada, Almeria and Getafe all in trouble.
Getafe boosted their hopes of staying up significantly, though, as Sergio Escudero grabbed the only goal in a 1-0 win over Sevilla.
Valladolid and Granada, who meet in the season finale, both lost.
Juanfran's last-gasp goal sent the former to a 4-3 defeat against relegated Real Betis, his strike coming after goals from Javi Guerra, Pena and Javi Guerra had offset a Pena own goal, plus efforts from Jorge Molina and Ruben Castro.
Granada, who had Jeison Murillo sent off in the 82nd minute, fell to a far less dramatic 2-0 home loss against Almeria - who boosted their own survival hopes via penalties from Verza and Aleix Vidal.
Osasuna, currently occupying the final relegation slot, were grateful for Javier Acuna cancelling out Diego Colotto's opener to earn a 1-1 with Espanyol, for whom a point was enough to secure top-flight football next year.
In the day's other game, Athletic Bilbao and Real Sociedad drew 1-1 as Imanol Agirretxe's 75th-minute equaliser ensured the spoils were shared after Iker Muniain had stuck for the hosts.