A solitary goal by Raul Garcia was enough to see off Valencia 1-0 and keep Atletico on course to finish as champions, with just three matches now left to play this season.
The midfielder headed in the crucial goal just moments before half-time and then Atletico dug deep to hold off intermittent swathes of pressure from Valencia to earn their first win at the Mestalla in 11 years.
They had to play the last minutes of injury time with 10 men after Juanfran was sent off for a reckless tackle, but it could not prevent them winning the game.
Barcelona remain four points behind Atletico after coming from behind on an emotional night at El Madrigal to beat Villarreal 3-2.
Playing their first game since the death of former coach Tito Vilanova, who succumbed to throat cancer aged 45 this week, Barca were subdued for much of the first half and trailed to a Ruben Cani goal scored on the stroke of half-time.
Manuel Trigueros then doubled the lead 10 minutes into the second half, but two Villarreal own goals sparked a comeback as Gabriel Paulista and Mateo Musacchio inadvertently brought things level before Lionel Messi struck the winning blow seven minutes from time.
Almeria gave their survival hopes a big boost by ending a run of four straight defeats with a come-from-behind 2-1 victory at nine-man Espanyol.
Christian Stuani put the mid-table hosts ahead just before the interval, but his dismissal shortly after the break was the catalyst for the visitors to turn the game on its head.
Fran Velez equalised in the 69th minute and, three minutes later, substitute Suso produced a stunning left-footed free-kick to lift Francisco's side up a place to 18th and within two points of fourth-bottom Getafe with three games remaining.
Javi Lopez was sent off in stoppage time to add to Espanyol's disappointing afternoon.
Athletic Bilbao have Champions League football in their sights after winning Sunday's showdown for fourth place against Sevilla 3-1.
Markel Susaeta set the hosts on their way by scoring straight from a corner in the fourth minute, and Iker Muniain strengthened their grip on the game with an acrobatic finish early in the second half.
A disappointing evening for Sevilla got even worse when Diogo Figueiras was sent off with 18 minutes remaining, and moments later Ander Herrera then added further shine to a convincing home win by heading in a third, although Kevin Gameiro reduced the deficit with 11 minutes to go.