The Minstermen dropped back into the bottom four ahead of Saturday’s home game with play-off qualifiers Forest Green and must look to take maximum points, while hoping either neighbours Guiseley, Torquay or Woking slip-up.
A draw against Forest Green could still be enough for Gary Mills’s men, but only if Guiseley are beaten at home by Solihull and Braintree fail to win at Aldershot.
Mills reasoned that Jon Parkin’s 75th-minute equaliser in Surrey, following Gozie Ogwu’s second-half penalty, could still prove decisive come the final reckoning.
“We’re looking at all scenarios now,” Mills admitted. “But we know we’ve got to win and, then, the point and Jon’s goal could be massive for us because, if Woking lose at Dagenham, we’ll go above them.”
An untidy contest at Kingfield saw Hamza Bencherif clear off the line at one end before blasting over from 10 yards at the other.
After the interval, Ugwu went on to convert his third penalty is as many games after Sean Newton had grabbed Delano Sam-Yorke’s shirt.
Parkin pounced for his 17th goal of the season when he drilled low to Michael Poke’s right from 10 yards after Sam Muggleton’s long throw fell to him in the area.
Woking: Poke; Thomas, Jones, Saah; Caprice (Dennon, 90), Murtagh, Ferdinand, Ralph; C Hall (Lucas, 70), Sam-Yorke, Ugwu. Unused substitutes: B Hall, Saraiva, Kretzschmar.
York City: Loach; Parslow, Bencherif, Newton; Holmes, Heslop, Hall, Whittle (Muggleton, 70); Oliver, Parkin, Morgan-Smith (Moke, 90). Unused substitutes: Simpson, Rooney, Connolly.
Referee: C Hicks (Surrey).