Martin Foyle's Minstermen are determined to go one better this time around after losing last May's play-off final to Oxford United.
But City were behind on 14 minutes, Callum Gittings on target for the visitors.
But the Minstermen grabbed an equaliser four minutes from full-time when Michael Rankine converted from the penalty spot.
Just when it looked likely to be enough for a point, the visitors were awarded a spot-kick of their own and Ton Shaw slammed home the winner.
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