The Minstermen made a blistering start and raced into a 2-0 lead inside the opening 10 minutes with two goals in a minute when Simon Heslop's corner was headed in by Sean Newton and then new signing Raul Correia robbed goalkeeper Ryan Schofield following a back-pass.
Former Wolves striker Sylvan Ebanks-Blake pulled one back for the Bucks on 21 minutes from a Ryan Wilson cross.
However, York went into the break 4-1 up, thanks to a second for Newton on 34 minutes and Adriano Moke shortly before the whistle.
As snow fell, Jonny Burn made it a nap hand for the visitors 7 minutes into the second half.
However, Ebanks-Blake's second of the contest on the hour-mark and another from Connor Johnson in the 71st minute meant it was a nervy finale for the visiting fans in the 852 crowd.
And they survived thanks to Adam Bartlett excelling to keep out Johnson's header and David Ferguson clearing off the line from John Marsden.
(Photo: Mike Sheridan)