The fifth-placed Blades face Yeovil over two legs after a dour match in which North End midfielder Lee Holmes came closest to a goal when his 67th-minute free-kick flicked off the top of the United crossbar.
The hosts thought they should have had a penalty in the 10th minute when teenager Joe Ironside went down under a challenge in the box but the claims were waved away by referee Steve Rushton before Kevin McDonald tested goalkeeper Declan Rudd from the resulting loose ball.
United winger Callum McFadzean was denied by Rudd three minutes into the second half and striker Ironside headed over moments later when well-placed.
The Lilywhites responded and almost edged ahead when Holmes’ right-wing cross picked out the head of Jack King, only for United keeper George Long to repel the striker’s close-range effort.
Blades’ substitute Chris Porter had the ball in the back of the net in the 62nd minute but his bundled finish was ruled out for handball, five minutes before Holmes struck the woodwork at the other end.