They trailed 2-0 at half-time and had Andrew Hughes sent-off after giving away the penalty for the Blades' second goal.
But a stirring second-half performance saw PNE reduce the deficit through Alan Browne's 71st minute goal after good work from Daniel Johnson.
Then in the 89th minute, Emil Riis slid home Ched Evans' cross for the equaliser.
Here on the player ratings on a night of high drama under the Deepdale floodlights, with Browne, Evans and Riis taking star billing.
13. Joe Rafferty 7
He joined the action as a half-time sub and played on the right, first as a wing-back and then a right-back. Contributed well. Photo: Camerasport
14. Ched Evans 8
Made a 25-minute cameo off the bench which helped swing the game PNE's way. His former club couldn't cope with his physical presence and what a peach of a cross for Riis' equaliser. Photo: Camerasport