Valencia beat Granada to boost their top-four hopes as Real Sociedad played out a thrilling 3-3 draw with Real Madrid, while all three relegation places remain undecided ahead of the final week of the season after Deportivo La Coruna lost to Malaga and Celta Vigo overcame Real Valladolid.
Elsewhere, champions Barcelona moved a step closer to claiming a club-record 100 points this season after beating derby rivals Espanyol 2-0 at the Estadi Cornella-El Prat.
Barca, who look set to seal the signing of Brazil superstar Neymar on Monday, were put on course for a 31st league win of the season through Alexis Sanchez's 14th-minute opener.
Espanyol's hopes of getting anything out of the match then suffered a blow when they lost Mubarak Wakaso to a red card in the 80th minute, and six minutes later Barca sealed the victory through substitute Pedro Rodriguez.
Tito Vilanova's men now need to beat Malaga in next weekend's final round of fixtures to become only the second side after Real Madrid to reach 100 points in a single season.
With the top three spots in La Liga already decided, the two-horse race for the fourth and final Champions League spot will garner much of the attention on the last weekend.
Valencia currently hold the upper hand after their 1-0 win over Granada, secured through Roberto Soldado's 60th-minute strike, saw them move two points clear of Real Sociedad, who drew 3-3 at home with second-placed Real Madrid.
Sociedad dominated almost from start to finish but had to battle back from 2-0 and 3-2 down just to get a point.
Madrid, who were without the injured Cristiano Ronaldo, went ahead through goals from Gonzalo Higuain (six minutes) and Jose Maria Callejon (57) but Sociedad deservedly drew level with strikes from Xabi Prieto (64, pen) and Antoine Griezmann (78).
Visitors Madrid soon resorted their lead through Sami Khedira but Sociedad battled back again and Prieto's second just before the final whistle earned them a point which could yet prove vital.
The relegation battle will also go to the wire with four clubs - Real Mallorca, Real Zaragoza, Celta Vigo and Deportivo La Coruna - fighting to avoid finishing in the bottom three.
Mallorca claimed a creditable 0-0 draw at third-placed Atletico Madrid while Celta were 2-0 winners at Real Valladolid, goals in either half from Gustavo Cabral and Iago Aspas earning the Galicians the points.
Both Zaragoza and Depor crashed to defeat, losing away to Europa League hopefuls Real Betis and Malaga, respectively.
Seventh-placed Betis won 4-0, with Ruben Castro opening the scoring inside 15 seconds and Dorlan Pabon (17, 71) and Jorge Molina (50) adding to the scoreline, while sixth-placed Malaga defeated Depor 3-1.
Javier Saviola (45), Julio Baptista (64) and Isco (80) struck for the Andalusian side with Depor's consolation coming from Diogo Salomao 15 minutes from time.
Those results mean that Osasuna are guaranteed another season of top-flight football after they secured a 2-1 comeback win over Sevilla.
Alvaro Negredo put Sevilla ahead just after half-time but Patxi Punal drew Osasuna level around the hour-mark and then substitute Alvaro Cejudo curled home a free-kick with 12 minutes remaining to earn the hosts all three points.
San Mames misery
Athletic Bilbao suffered disappointment in their final league game at their famous San Mames stadium as they went down to a last-gasp goal to Levante.
Juanlu struck the winner in stoppage time after Athletic had lost striker Iker Muniain to a 62nd-minute sending off.
In Sunday's other game, Diego Castro's late own goal saw eighth-placed Rayo Vallecano win 2-1 at local rivals Getafe.
Alejandro Dominguez cancelled out Rafa Lopez's opener before Castro put through his own net to earn Rayo the spoils.