Barnet slipped to second spot in the Vanarama National League after being held 1-1 by Halifax at The Hive.
Billy Waters turned in Jamie Cooke’s 11th-minute cross for his fifth goal of the season to give the Yorkshire visitors a shock lead.
Barnet levelled after 24 minutes through Mark Shelton’s shot from outside the box, which Sam Johnson was unable to stop.
Shelton saw another first-half effort cleared off the line, while Florent Hoti went close for Halifax late on with a free-kick that skimmed the crossbar.
York’s 3-0 home victory over Southend took them above Barnet and into top spot on goal difference.