Vale looked to be heading towards a shock victory in League Two on Saturday after defender Lee Collins fired them into a 61st-minute lead, but Chairboys boss Peter Taylor made what proved an inspired substitution when John-Paul Pittman replaced John Akinde.
Pittman had been on the field for less than two minutes before making a rampaging run to the touchline and setting up a simple tap-in for the onrushing Sawyer.
Wycombe midfielder Matt Bloomfield went closest to breaking the deadlock after nine minutes when his fierce shot was well saved by Vale goalkeeper Chris Martin.
But Vale shocked Taylor's men when Collins pounced after Paul Marshall's corner had sailed through a crowded area to the far post.
Vale squandered a great chance to go two goals up shortly after when Jamie Young plunged to save at the feet of Danny Glover - and they were made to pay by Sawyer's late strike.