David Allasan and Cameron Morfoot were on target, with the latter’s winner coming in the closing stages.
It was a pleasing win for United, who kept going right through until the end to seal the three points - like they did three weeks earlier in the home season opener against Chesterfield, when they showed character to come back from two goals down and won 3-2.
Allasan scored in the opening minutes. It was a well-worked goal, as he was fed through down the right side of the 18-yard box and coolly finished into the bottom corner.
There were further opportunities to score, but the Minstermen levelled later in the opening half.
The winner arrived in the last moments, as a free-kick was put in and Kane Bartholomew headed the ball across the box. Morfoot was then there to convert home the winning goal, capping a solid defensive display from himself.
It was a hard-earned win, and the aim now is for standards to remain high and to keep improving.
Team: Kelsey, Harrison, Bartholomew, Hornshaw, Lilley, Morfoot, Busby (Ablett, 45), Pugh, Collins, Allasan, Train (Okafor, 70).
Substitutes not used: Riches, Kalu, Colclough.