The comprehensive victory meant the Cucumber Growers are safe from relegation, with their hosts fluffing a chance to move clear of fourth-placed Getafe in their bid for a Champions League spot next season.
En-Nesyri, with his ninth goal of the season, opened the scoring eight minutes into the encounter, despatching one into the top corner.
Failure to clear a long throw-in into the box saw Martin Braithwaite pounce to double the visitors’ lead in the 20th minute.
With eight minutes left on the clock, the Denmark international set up Oscar Rodriguez, who wrapped up an important victory with his strike.
Leganes are now placed ninth on the La Liga table after collecting 45 points, 10 clear of the relegation zone.
The Atlas Lions have been placed in Group D alongside Cote d’Ivoire, South Africa and Namibia.