كتب : Hatem Maher
The result put Real in sixth place on 30 points, trailing leaders and defending champions Barcelona with massive 13 points.
Juan Roman Riquelme almost put Villarreal in front in the 22nd minute after a fine exchange with Juan Pablo Sorin before curling a brilliant drive but it went just beside the post.
Three minutes later, Uruguayan international Diego Forlan sent a powerful first-timer from the edge of the box but it was just inches wide.
Julio Baptista squandered a rare chance for Real in the 29th minute when he went face-to-face with Villarreal keeper Sebastian Viera before slamming the ball far from the net.
Earlier on Sunday, Cadiz beat Getafe 1-0, Celta Vigo edged Real Sociedad 1-0, Real Zaragoza defeated Alaves 2-0.
In other matches, Mallorca drew 1-1 with Real Betis, Osasuna tied Racing Santander 1-1 and Sevilla cruised past Malaga 3-1.