Raul Garcia's 18th goal of the season in all competitions made the difference for Diego Simeone's men, who need a further six points to guarantee the title.
Garcia scored in the 43rd minute with a header from Gabi's cross and the visitors to Mestalla managed to hold on despite Juanfran's late red card.
Barca found themselves behind at the break after Cani's clever finish and Manuel Trigueros doubled Villarreal's lead early in the second half with a firm header.
The fight for the final UEFA Champions League spot looks to have been won by Athletic Bilbao after Ernesto Valverde's men defeated challengers Sevilla 3-1 at San Mames, moving six points clear of the Andalusians.
Sevilla full-back Diogo Figueiras received a second yellow card for arguing with officials in the 72nd minute and Ander Herrera scored Athletic's third a few moments later, before Kevin Gameiro struck a late consolation.
Almeria's chances of avoiding the drop received a boost in Sunday's early match as they beat nine-man Espanyol 2-1 in Barcelona.
Fran Velez and Suso grabbed the goals as the visitors came from behind to secure the win, but Christian Stuani's 48th-minute red card gave Almeria a helping hand, while Javi Lopez also received his marching orders in second-half stoppage time.
