Lawrie Dudfield had twice put the travelling City ahead, with Michael Oliver and Patrick McCourt levelling ahead of a 64th minute winner from Kevin Townson.
Mansfield Town, who looked certain to be claiming automatic promotion a few short weeks ago ensured they will finish in the top seven by virtue of a 2-1 triumph over third placed Cheltenham Town.
Greenacre and White were the goalscorers for the Stags, a win that moves them upto third although Cheltenham have two games in hand to reclaim that third automatic promotion spot.
York City and Carlisle United, who were featured earlier today in this section, played out a goaless draw at Bootham Crescent.