Alan Browne's 57th minute goal settled the contest in PNE's favour in South Yorkshire, the Irishman netting from six yards after a shot from Josh Harrop had been parried by Blades goalkeeper Jamal Blackman.
They had the ball in the net a second time 11 minutes later but substitute Tom Clarke's header was ruled out by an offside flag.
North End had plenty of defending to do as the home side piled on the pressure in search of an equaliser as the clocked on but protected Declan Rudd very in the main - Rudd having to make a good save from sub David Brooks.
With Derby County drawing 1-1 at Aston Villa, it left North End two points behind the Rams with a game to play - everything is on next Sunday's home clash with Burton Albion.
Neil had made four changes to the PNE side, Ben Davies, Daniel Johnson, Harrop and Sean Maguire coming into the team - out went Clarke, Paul Gallagher, Tom Barkhuizen and Billy Bodin.
The visitors started with a diamond-shaped midfield, Ben Pearson sitting deep with Browne and Johnson ahead of him, Harrop at the forward point behind front two Maguire and Callum Robinson.
A lively start saw a couple of half chances come North End's way, Harrop's free-kick from the right channel in the 10th minute finding Paul Huntington in the box who could only loop a header up into the keeper's gloves.
Robinson then got some room down the left to cut inside into the box but his shot was blocked by the covering Lee Evans.
Huntington made a good sliding block to take a shot from Leon Clarke behind as the Blades threatened properly for the first time with a quarter of an hour played.
The half developed into something of a nervous affair, with neither side able to get a pattern to their play.
PNE keeperRudd blocked Clarke's toe-poke at close quarters after Enda Stevens had forced his way down the left side of the Preston box and pulled it back into the striker's path.
Just before the interval, home midfielder John Fleck hit a powerful drive from outside the box which Greg Cunningham threw himself in the way of to block with his head and send it behind for a corner.
Early in the second half, Maguire's run took him down the right hand side of the box, his low shot blocked by a defender in the six-yard box as Robinson looked to get contact on it.
The deadlock was broken in the 57th minute as Browne notched his ninth goal of an impressive campaign.
Harrop got the ball 25 yards out, stepped forward and hit a low right-foot shot which Blackman dived to his left to parry.
First to the rebound was Browne who swept it into the net from six yards in front of the 1,610-strong travelling Preston support.
Straight after the goal Barkhuizen replaced Maguire, that substitution having been got ready before the goal.
After seeing out a spell of pressure in which North End cleared three corners in quick succession, the visitors made a double change with Clarke and Gallagher coming on for Johnson and Harrop.
It saw them switched to three at the back to match-up their hosts' system.
Clarke's first contribution was at the other end, putting the ball in the net from Barkhuizen's header after he had met a free-kick.
But the flag was up for offside against the skipper to cut the celebrations short.
A fine save from Rudd denied the home side in the 76th minute, the keeper getting fingertips to a shot from Brooks to help it over the bar.
North End had to soak up plenty of pressure from the Blades in the closing stages but held out with some strong defending and some rather cynical time-wasting - Rudd getting a yellow card for taking too long taking a goal kick.
Robinson almost made for a more comfortable finish in stoppage-time when he found room behind the Blades defence and saw his shot from the edge of the box tipped over by Blackman.
Sheffield United: Blackman, O'Connell, Stearman (Leonard 80), Basham, Freeman (Baldock 76), Fleck, Evans (Brooks 66), Duffy, Stevens, Clarke, Sharp. Subs (not used): Lundstram, Donaldson, Lafferty, Moore.
PNE: Rudd, Fisher, Huntington, Davies, Cunningham, Pearson, Browne, Johnson (Clarke 67), Harrop (Gallagher 67) Robinson, Maguire (Barkhuizen 58). Subs (not used): Moult, Earl, Bodin, Maxwell.
Referee: James Linington (Isle of Wight)
Attendance: 28,569 (1,610 PNE)