The crucial goal came on 23 minutes, Delano Sam-Yorke firing in a long-range effort.
Defeat means the Lions are in the relegation zone, a point behind fifth-from-bottom FC Halifax Town, with one game remaining
Their final game is next Saturday at 5.30pm, when they host Torquay United.
Halifax are at home to Macclesfield, while Boreham Wood - on the same points now as the Shaymen - travel to Welling.
For all the latest from today’s games, check out The Yorkshire Post’s live feed by clicking the link below....