Morgan scored his first spot kick in the third minute after being fouled by Scott Kerr before repeating the trick on the stroke of half-time when Jamal Fyfield barged over Joel Grant.
Wycombe didn't let up and netted a third through Grant just before the hour while Dave Winfield completed the rout 10 minutes from time.
Morgan dispossessed Kerr on the edge of the area early on and drew a foul from the backtracking midfielder before burying the penalty into Michael Ingham's left corner.
The 29-year-old fired his second into the middle of the net after Fyfield floored Grant, who was to score a superb solo effort after the break.
Grant passed the ball around outstretched York keeper Ingham at the far post following a piercing run that started on the right wing.
York striker Jason Walker then volleyed over from six yards before Winfield headed a fourth high into the middle of the goal from Josh Scowen's 78th-minute corner.