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.
Then in the 89th minute, Emil Riis slid home Ched Evans' cross for the equaliser.
5. Ben Whiteman 7
His play was slightly off radar in the opening stages but the midfielder got better as the game went on. Had a much better second half. Photo: Camerasport
6. Brad Potts 6
Potts didn't do too badly in the right wing-back slot and briefly switched to the left towards the end of the first half. He was subbed at half-time. Photo: Camerasport
7. Alan Browne 9
Did the skipper stop running for just one moment? Drove PNE on as they chased the game and produced a good finish for the first goal. This was Browne at his best. Photo: Camerasport
8. Daniel Johnson 7
The midfielder produced the cross to set up PNE's first goal. Didn't really happen for him in the first half but DJ was far better in the second - in line with many of his team-mates. Photo: Camerasport