Having impressed in qualifying for the Europa League quarterfinals 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 place as Valencia dropped down to fourth.
Unai Emery's side have now lost their last two league games since being knocked out of Europe's elite club competition.
Espanyol fell 2-0 at lowly Malaga. Jose Rondon scored twice to boost Malaga.
In other games, Racing Santander's forward Giovani Dos Santos 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 Coruna.
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