Valencia suffered a 4-0 hammering at Espanyol in La Liga on Sunday to dent their Champions League aspirations.
Christian Gomez, Verdu, Alvaro Vasquez and Kalu Uche scored for the home side, who earned their first win in six games in some style.
Espanyol are within reach of a Europa League place in 10th place, but just one point behind sixth-placed Osasuna, while Valencia's travails continue with the loss meaning they have just four wins in their last 12 league games.
They remain third but only by a point ahead of Malaga, who drew 1-1 with Real Sociedad.
Isco Alarcon opened the scoring for Malaga but they could not hold on as Xabi Prieto equalised for Sociedad.
Athletic Bilbao's preparations for their Europa League semi-final on Thursday received a boost with a 1-0 over Mallorca courtesy of Fernando Llorente's 28th goal of the season.
The Spanish international headed through the legs of goalkeeper Dudu Aouate after only 12 minutes with the only goal of the game.
Atletico Madrid gave their hopes of qualifying for the Europa League a boost with a 1-0 away win at Rayo Vallecano.
A goalkeeping blunder from Rayo 'keeper David Cobeno handed Atletico the win, after he came off his line to attempt a clearance from striker Falcao, but got to the ball second and allowed the Colombian to easily take the ball past him and fire home.
The win leaves Atletico in ninth place, just one point behind Osasuna in the race for a Europa League berth.
Real Zaragoza moved within five points of safety with a 1-0 win over nearest rivals Granada.
Real Betis outplayed 10-man Osasuna in a 1-0 win at home thanks to Ruben Castro's 33rd-minute strike.
A last-gasp equaliser from Lautaro Acosta earned a 1-1 draw for Racing Santander against Villarreal.
Racing are still 10 points from safety while the two dropped points deprived Villarreal the chance to pull further clear of the drop zone.