Mansfield took an early lead when Matt Rhead was allowed to plant a free header past Matt Ingram, but Wycombe drew level through a controversial Paul Hayes spot kick after Martin Riley was adjudged to have handled in the area, when he appeared to be just outside it.
Hayes had a hand in the winner too, flicking on a Joe Jacobson cross from the left for midfielder Peter Murphy to nod in at the far post, which he collided with in the process of scoring.
Manager Gareth Ainsworth said: "The way we saw the game out was something else. The players and fans have all gone home without an ounce of energy left in them, and that's what we want to build here. They are knowledgeable fans, and they could feel today the steps we have taken. Last season we would have lost that game.”