Valencia scored with their only shot on target to come away from the capital with all three points after containing the hosts for periods of the game.
Leganes controlled the majority of play in the first half but they rarely threatened Jaume Domenech in the Valencia goal.
The second half didn’t improve much on the first but just beyond the hour mark there was a goal to lighten the game up somewhat, Ruben Perez tried to bring the ball clear for Leganes but he was dispossessed with the ball falling to Rodrigo Moreno who made himself a yard of space before drilling a powerful low shot with his left foot into the bottom right hand corner.
That was it from Valencia in terms of attacking threat with Leganes now having to press in search of an equaliser.
The closest they came was in the 83rd minute when Claude Beauvue collected the ball in the area and laid it off to Nabil El Zhar but his shot was blocked from close range by a Valencia defender and Los Che were able to hang on for the win.
Defeat sees Leganes’ slim hopes of Europa League qualification all but over but Valencia stay fourth, just a point behind Real Madrid.
Leganes: Cuellar; Zaldua, Bustinza, Munoz (Beauvue, 73), Siovas, Rico; Eraso, Perez, Gabriel (Naranjo, 90), Omar (El Zhar, 79); Amrabat
Valencia: Jaume; Vezo, Garay, Gabriel, Gaya; Soler (Torres, 65), Parejo, Kondogbia, Guedes (Pereira, 80); Zaza (Vietto, 70), Rodrigo