In front of City's best crowd of the season, York almost got the perfect start when a cleverly worked corner between Darren Dunning and Clayton Donaldson picked out Emanuel Panther who shot over from ten yards.
Both sides attacked in a game played at a terrific pace with plenty to excite the crowd. Andy Bishop glanced a header inches wide from Mark Convery's free-kick, and then put the Minstermen ahead on 36 minutes.
Bishop fed Jamie Price on the right and was there to receive Price's pull-back from the byline to drill home from eight yards.
Dave Merris was unlucky not to put City two up when his shot from 25 yards was pushed round the post by keeper Tony Roberts.
City lost their way a little in the second period, buckling under intense pressure from the visitors.
Tresor Kandol was unlucky with a glancing header from an early corner and was unlucky again when defender David McGurk cleared his shot off the line with keeper Chris Porter beaten.
City hit back late on, with Donaldson and Joe O'Neill both having good efforts blocked. Donaldson almost sealed the points for City in the closing stages, showing great skill on the edge of the box, but saw his shot brilliantly saved by Roberts.
Then at the death, the home supporters were silenced by Griffiths' stunning equaliser.