The home side got off to a nightmare start when a catastrophic mix-up between defender Chidozie Awaziem and goalkeeper Ivan Cuellar allowed Turkish forward Enes Unal to pass the ball into an empty net in the second minute.
Valladolid looked in control for most of the game and doubled their lead when Ruben Alcaraz lashed high into the net in the 54th minute, although Leganes pulled a goal back in the 84th with a penalty from Oscar Rodriguez.
Leganes had a half-hearted appeal for a second spot kick late on for handball when a Valladolid defender chested a cross away, but with no home fans to cheer the team on, they mustered little else in the final stages of the game.
Leganes are 19th on 23 points after 28 games, level with bottom side Espanyol who beat Alaves 2-0 earlier on Saturday. Valladolid meanwhile moved up to 14th on 32, seven points clear of the relegation zone.
Leganes coach Javier Aguirre said his side struggled to cope with the setback of going behind so early in the game.
"The first goal was a very tough blow and we were left shaken for a long time. We made few mistakes overall but it means little and we cannot afford to give away a goal like that," he told a virtual news conference.
"We've wasted a golden opportunity because this game was a six pointer and as we were at home we should have taken the fight to them. But we're not dead yet and we all have to keep on fighting together."