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.
1. Daniel Iversen 7
The PNE keeper made two very good saves from Ndiaye in either half and one low down from Brewster. The first goal which beat him seemed to catch a deflection, Photo: Camerasport
2. Sepp van den Berg 7
The defender was his usual energetic self and was always prepared to push up out of defence to get PNE on the attack., Photo: Camerasport
3. Patrick Bauer 6
Stuck to his task at the back against Brewster and Sharp who were a handful in the first half. Made some good clearances at set pieces. Photo: Caemrasport
4. Andrew Hughes 5
The defender got his marching orders in the 38th minute for a foul on Brewster in the box. It was a penalty but maybe not worthy of a red card. Had done okay until then. Photo: Camerasport