Diego De Girolamo’s strike in the 85th minute meant The Bucks progress to the next round of the FA Cup.
Buxton started the better of the 2 sides with handball calls in the first minute after Jamie Ward’s shot but the ref waved them away.
Only minutes later Warren Clarke laid Diego off for a shot that he dragged just wide of the mark.
York then responded well with Paddy McLaughlin hitting a volley from the edge of the area.
The Minstermen’s best opportunity of the half came on the 23rd minute a header from former Hull player Clayton Donaldson forced Theo Richardson into an outstretched save.
Olly Dyson also came close as his low driven shot went just past Richardson‘s post in goal
It was Buxton though who ended the half as the more dominate side. Chris Dawson making Jameson tip it over the bar with a looping shot that was dipping in.
York almost gained the lead through a Sam Fielding header from a freekick but Richardson got down well to save again.
The Bucks, who had over 1000 fans in attendance, pushed forward again with Diego trying to dink the ball over the goalkeeper.
And it was Diego who grabbed the winning goal on the 85th minute with Former York player Ash Chambers playing it across to Diego who curled his shot into the back of the net sending the away fans into an eruption of cheers!
City thought they had an equaliser as substitute Gilchirst but the ball into the net following a long throw but the ref called it back for a foul on a Buxton player.
Buxton now progress to the second round of the FA Cup and are in the draw on Monday night.