The Minstermen took the lead in the 13th minute from the penalty spot after a fantastic burst into the box from Alex Rodman with Jason Walker easily converting for his seventh goal of the season.
Ten minutes before half-time, the hosts doubled their lead through Patrick McLaughlin as Burton goalkeeper Dean Lyness palmed away Walker's in-swinging corner into the path of the midfielder for the simplest of finishes.
In first-half stoppage time Burton came close to reducing the deficit with Billy Kee forcing a full-stretch save from Michael Ingham before Michael Potts blocked Aaron Webster's opportunist flick on the line.
Burton again went close after the restart with York defender Chris Smith producing a fantastic double block on the line from Kee and Marcus Holness. With ten minutes left City wrapped up the victory as Matty Blair fired in from distance to give the Minstermen their first win of the festive period.