Jebbison, on loan from Bournemouth, silenced the jeers from the visiting United fans at Deepdale with a headed winner in the 58th minute.
Andre Brooks had put the Blades ahead with his first goal of the season after 10 minutes, and Callum O'Hare's scintillating solo effort doubled the advantage six minutes later.
But Lewis Dobbin halved the deficit from just outside the area in first-half stoppage time.
Japhet Tanganga's own goal less than a minute into the second half set up the big escape act from Paul Heckingbottom's men against the club he has twice managed.
Preston climbed to fifth place in the Championship, while United sit one point above the relegation zone.