Dave Winfield's 73rd-minute effort settled the contest in York's favour, putting them five points clear of danger and bottom club Cheltenham three adrift of safety.
The revival of Ronnie Moore's Hartlepool United - who had won four in a row to climb out of the drop zone - stalled somewhat as they drew 2-2 at Newport County after throwing away a two-goal lead.
Moore's men remain a point ahead of Tranmere Rovers, who occupy the second relegation place after squandering a 2-1 advantage in their 2-2 stalemate at Stevenage.
Carlisle United remain in the dogfight despite Charlie Wyke's 95th-minute leveller in a 2-2 draw with Portsmouth, while Cambridge United are still looking nervously over their shoulders following a 2-0 home defeat to Bury.
Bury's triumph moves the Lancashire club within four points of third-placed Wycombe Wanderers, whose automatic promotion hopes were hit by a double from Kemar Roofe in a 3-2 home reverse to Oxford United.
Burton Albion are just a point clear at the top after Carl McHugh salvaged a 1-1 draw for Plymouth Argyle four minutes from time, Shrewsbury Town closing the gap thanks to Connor Goldson's double in a 2-0 victory over Dagenham and Redbridge.
Luton Town's winless run was extended to seven games in dramatic fashion as David Wheeler scored the decisive goal in the fifth minute of added time in Exeter City's 3-2 win at Kenilworth Road.
Elsewhere, Southend United beat Mansfield Town 2-0, Laurence Wilson missed a penalty in Morecambe's 1-1 draw with 10-man Accrington Stanley and AFC Wimbledon were held to a 2-2 draw by Northampton Town.
