A solitary goal by Raul Garcia was enough to see off Valencia and nudge Atletico Madrid closer still to the Primera Division title.
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 Mestalla in 11 years, 1-0.
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.
This was widely believed to be Atletico's toughest test remaining and the fact they came through it will only strengthen their confidence of holding off the challenge from Real Madrid, who they lead by three points.
Diego Simeone's side now need just two wins from their next three games to lift their first league title in 18 years.
Barcelona came from two goals down to beat Villarreal 3-2 and stay in the title race on an emotional night for the club.
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 killer blow seven minutes from time.
The result leaves Barca four points behind Atletico with three games to go. The pair face off on the final day of the season.
Athletic Bilbao have Champions League football in their sights after winning Sunday's showdown for fourth place with 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.
Sevilla went into the game three points behind Athletic and an away victory would have unseated the Basques in fourth, but now Ernesto Valverde's side enjoy an almost unassailable six-point lead in the position, and a win next week at Rayo Vallecano will secure their place in next season's Champions League
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.