Buoyed by their recent good run of form, the Minstermen took the lead in the seventh minute with Ryan Bowman scoring from the penalty spot for the second successive game after Josh Carson was fouled by Sam Togwell.
City had the ball in the net four minutes later with Keith Lowe heading home Will Hayhurst's corner but the referee disallowed the goal for a foul in the area.
Wycombe struggled to deal with York's relentless pressure and the hosts eventually doubled the lead on half-time with Hayhurst feeding Carson who fired home from the edge of the area.
Wycombe almost set up a frantic finale with nine minutes remaining with Craig striking the post when clean through on goal.
Their misery was compounded in the final minute of stoppage time with debutant Togwell receiving a second yellow card for a foul on York substitute Lewis Montrose.