Two goals apiece from Juan Mata and Roberto Soldado either side of an Ever Banega strike moved Valencia on to 60 points with seven matches left to play, six ahead of fourth-placed Villarreal.
Champions Barcelona are top with 84 points after coming back to beat Almeria 3-1 with a double from Lionel Messi on Saturday.
Spain winger Mata streaked away to double the advantage in the 55th and Villarreal crumbled with Thursday's 5-1 Europa League quarter-final first leg victory over Twente perhaps taking its toll. Banega scored from a Pablo Hernandez pull-back, Mata tapped into an open goal and Soldado lobbed Diego Lopez to complete the rout in the 76th.
Filipe Luis opened the scoring with a fierce drive early on, Jose Antonio Reyes produced a wonderful piece of skill to set up Mario Suarez before the break and Argentina's Sergio Aguero sprinted clear to seal the points 12 minutes from time.
The holders were knocked out of this season's Europa League at the group stage in December.
Espanyol's steady slide out of contention for the European places continued on Sunday with a 0-0 draw at Hercules that saw them slip to eighth on 44 points. They host Atletico next weekend.
David Barral pounced on an error to score in the second half as Sporting rose to 11th with 38 points. Hercules remain in the relegation places in 18th with 30 points, ahead of Malaga on goal difference, after Manuel Pellegrini's side drew 0-0 at home to 10-man Deportivo La Coruna.
