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.
9. Tom Barkhuizen 6
While Bakrhuizen has played a variety of roles for PNE, left wing-back was a new one for him. He was better when played on the right in the second half. Photo: Camerasport
10. Scott Sinclair 5
Starting up front, Sinclair saw an early shot saved which really he should have put away. Was subbed after 38 minutes following Hughes' red card, sacrificed so a defender could come on. Photo: Camerasport
11. Emil Riis 8
The Dane had his best game yet under Ryan Lowe and was PNE's last-gasp hero in netting the equaliser. Riis had a couple of other chances to score before that. Photo: Camerasport
12. Greg Cunningham 7
Got an earlier than expected shout off the bench when Hughes was dismissed. Equipped himself well when he came on, almost set up a goal late on with a ball across the face of the goal. Photo: Camerasport