Ryan Manning's fine finish from 25 yards settled the contest in the home side's favour.
The goal came six minutes into the second half, during a spell when the Jacks had their best spell of the game.
With such a slender margin between the sides, there was always the chance of North End finding their way back into it.
They saw a lot of the ball in the closing stages but clear-cut chances were lacking, with crosses being blocked or moves breaking down in and around the box.
Substitute Ryan Ledson saw a shot hit his team-mate Greg Cunningham almost on the line deep into stoppage-time, that perhaps summing-up PNE's luck on the day.
The first half had been nip and tuck, a couple of opportunities at either end but little to separate the sides.
Swansea got on top early in the second half, Daniel Iversen needing to make a couple of fine saves after Manning's goal.
It was a first league defeat for North End under Ryan Lowe after two wins and two draws previously.
The North End side had shown three changes to the XI which started the 2-2 draw with Sheffield United.
Joe Rafferty, Ched Evans and Cunningham came into the side, Scott Sinclair dropping to the bench while Brad Potts was injured and Andrew Hughes was suspended.
Rafferty started at left wing-back, with Tom Barkhuizen in that wide role on the right.
Cunningham filled the vacancy created by Hughes' ban on the left side of the back three, with Evans partnering Emil Riis up front.
It was Swansea who settled into the game more quickly than PNE, looking very comfortable on the ball .
Much of their play went through Joel Latibeaudiere and Olivier Ntcham down the left, seemingly in a bid to try and find space before Barkhuizen and isolate Sepp van den Berg.
The hosts had a seven minute chance when Daniel Iversen misplaced a pass out from the back and it fell to Ntcham on the left side of the box who fired into the side-netting.
North End started to pick up some momentum and went close to scoring in the 14th minute.
A ball over from the left travelled across the box to Barkhuizen who lifted a cross back into the middle. Evans rose to meet it and got a header away which Jacks goalkeeper Ben Hamer tipped over the bar.
Matt Grimes lifted a shot over the bar from the edge of the box at the other end, Swansea having played their way up field and worked the ball down the left.
A chance fell PNE's way when Hamer slipped making a clearance and the ball landed to Daniel Johnson's feet 30 yards out. Johnson hit a low shot first-time which went just wide of the target,
There was a blow for North End nine minutes before half-time when Barkhuizen came out second best in a challenge with the sturdy Ntcham.
He stayed on the pitch while PNE got Matthew Olosunde ready to come on, Barkhuizen actually managing a sprint down the right-wing in that time.
But he had to come off, allowing Olosunde his first appearance since early December.
Two minutes into the second half, Ben Whiteman's low curling shot from the edge of the box went wide of the far post.
Swansea took the lead in the 51st minute, it being a goal somewhat out of the blue.
North End partly cleared their lines after a cross came into their box from Swansea's right. The ball fell to Manning 25 yards who struck a superb shot past Iversen.
Three minutes later they almost got a second, Swansea counter-attacking down their left side and working the ball across the face of the box.
Cyrus Christie left fly with a shot inside the box which Iversen dived to push behind..
Another Christie shot curled just wide and Manning was denied by an Iversen save as the home side began to find ways through the PNE back line.
North End boss Lowe opted for a change in personnel and formation in the 65th minute, Scott SInclair replacing Rafferty.
Sinclair went on the right hand side of a three-man front line in a 4-3-3 system..
A chance fell PNE's way soon after the change, Riis chasing a ball down the left channel and playing in Alan Browne ahead of him.
Browne cut back a cross into the path of Johnson, the midfielder's shot blocked by a defender sliding across him.
In the closing stages it was all PNE as they went in search of an equaliser and Swansea put men behind the ball.
Ledson came on as the final substitute, replacing Whiteman with six minutes left.
It was Ledson who had a late sight of goal, his shot from outside the box after Riis' throw in had been cleared seemingly on target until it struck team-mate Cunningham and flew wide.
Swansea: Hamer, Cabango, Naughton, Manning, Christie (Fulton 84), Downes, Grimes, Latibeaudiere, Smith, Ntcham (Wolf 46), Piroe (Joseph 74). Subs (not used): Fisher, Bennett, Obafemi, Walsh.
PNE: Iversen, Van Den Berg, Bauer, Cunningham, Whiteman (Ledson 84), Rafferty (Sinclair 63), Browne, Johnson, Barkhuizen (Olosunde 36), Riis, Evans. Subs (not used): Ripley. Lindsay, McCann, Maguire.
Referee: Josh Smith (Stamford)
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