Ruben header sends Villarreal third
Having impressed in qualifying for the Europa League quarter-finals by beating Bayer Leverkusen on Thursday, Villarreal appealed more to their battling qualities to move up to 54 points with nine games left.
They took possession of the last automatic Champions League qualification place as Valencia dropped down to fourth on goal difference.
Unai Emery's side have now lost their last two league games since being knocked out of Europe's elite club competition.
Bilbao slipped further off the top four in sixth with 42 points, one behind a fading Espanyol who fell 2-0 at lowly Malaga.
On Saturday, leaders Barcelona moved on to 78 points after beating Getafe 2-1 at home, maintaining their five-point lead over title rivals Real Madrid who won 2-1 at derby rivals Atletico Madrid.
An industrious Borja Valero created the opening for Ruben to score at Bilbao after 58 minutes, the Argentine striker powering a superb header beyond Gorka Iraizoz.
Villarreal clearly tired as the second half progressed, but for all Bilbao's pressure they could not find a way past visiting goalkeeper Diego Lopez.
Valencia and Sevilla played at a frenetic pace at Mestalla with both sides hitting the woodwork twice and it was a surprise a goal did not arrive until the 70th minute.
Croatia midfielder Rakitic pounced on a loose ball to fire Sevilla ahead but they also had to thank goalkeeper Javi Varas for pulling off a string of spectacular saves.
Sevilla, who drew 1-1 with Barca last week, are seventh with 42 points but below Bilbao because of an inferior head-to-head record.
At the foot of the table, Jose Rondon scored twice to boost Malaga's bid for La Liga survival in a 2-0 home win over Espanyol.
The Venezuelan striker made the most of a defensive error to net early on and finished off a flowing attacking move in the 26th minute to make it two wins from two for Manuel Pellegrini's outfit.
Malaga climbed to 18th in the standings with 29 points, one point from safety, ahead of Almeria and Hercules who both lost to stay on 26 points.
Free-falling Hercules hit the foot of the standings after a 4-0 thrashing at home to Osasuna, a fourth straight defeat, which saw their coach Esteban Vigo sacked.
Almeria are 19th due to a superior head-to-head record after losing 1-0 at Sporting Gijon.
In other games, Racing Santander's Mexican forward Giovani dos Santos, on loan from Tottenham Hotspur, slid in to grab the decider in a 2-1 home win over Real Sociedad and Ruben Suarez's last-minute free-kick gave Levante a 1-0 win at Deportivo La Coruna.