It appeared as if York would be bringing an end to a run of seven games in all competitions without a win when David McGurk netted in the 64th minute.
But the lead lasted just six minutes as Morgan reacted quickest to Matt McClure's shot cannoning back off a post for a simple tap in to earn a draw.
Marvin McCoy fired just wide as Wycombe started confidently but York grew into the first half and Lanre Oyebanjo saw a 35-yard effort drift over in the 17th minute.
And it was Wycombe's goalkeeper Matt Ingram who was the first to be called into action to deny Wes Fletcher from just outside the box seven minutes before half-time.
The second half burst into life as McGurk lost Kortney Hause at the back post from a Ryan Brobbel free-kick to head home before Morgan's awareness earned the Chairboys a point.