The Lilywhites dominated from start to finish as Melle Meulensteen broke the deadlock with a first-half penalty before an Alex Wood strike and an own goal extended the margin of victory after the break.
The hosts started with purpose, consistently winning the ball back high up the pitch, and that strategy almost led to the opener in the sixth minute.
Mike Howard regained the ball on the right for PNE and delivered a superb crossfield pass to Josh Earl, who saw his low strike well saved by Wrexham goalkeeper Owen Kirkham one-on-one.
Harry Garstang nearly scored from a free-kick in the 11th minute, curling over the wall from a central area towards the bottom left corner, only for Kirkham to tip it behind for a corner.
Melle Meulensteen had a shot blocked soon after, while Tommy Creamer’s effort from distance was comfortably saved by Callum Roberts at the other end.
Then came the breakthrough in the 20th minute, as Earl caused mayhem with his run into the box and was awarded a penalty after being brought down. A composed Meulensteen made it 1-0 by finishing low into the bottom left corner from the spot.
North End looked comfortable and had further chances as Earl’s shot from just outside the box was blocked and Kamol Campbell also had an effort diverted away from goal, while the visitors could only threaten from distance as Brandon Burrows put one over the bar.
Howard showed quality on the right again shortly before the break, with his delayed cross finding Garstang in space only a few yards out – but his header was superbly kept out by Kirkham.
The pair nearly combined again on the stroke of half-time when Garstang won it back in a dangerous area but played a cross from the left just in front of an outstretched Howard.
The Lilywhites overcame a brief resurgence from Wrexham after the interval to double their lead in the 61st minute, with substitutes Wood and Ethan Walker playing a key role in the goal.
Walker had come on just seconds before he cut in from the left and passed to Garstang on the edge of the box, who then fed Wood to his right to finish with a brilliant first-time effort placed neatly inside the bottom-left corner.
Walker was involved again minutes later as his shot towards the top-right corner was palmed away before Garstang’s effort flashed past the post from outside the area.
With 20 minutes remaining, Earl almost provided a third for PNE after a brilliant run down the left, but his cross was parried and no-one could connect for a rebound.
Wrexham continued shooting from distance, with Scott McHarrie twice putting efforts over before forcing a brilliant save from Callum Roberts with a fierce drive in the closing moments.
Wood went close from 25 yards out in the latter stages as well but curled just wide of the far post after cutting in from the right.
Leon Creech then saw an effort flash past the post via a deflection late on before fellow full-back Earl showed great determination to create PNE’s third deep into stoppage time.
Earl drove down the left, beat his man at the byline and put a tremendous chipped cross into the six-yard box, with a Wrexham defender turning the delivery in from a few yards out.
That sealed a comfortable win for the Lilywhites and academy manager Nick Harrison was pleased with the display.
“I thought we played really well in the conditions,” he said. “The pitch was soft but I thought we played some really good football, passed it really well and in all honesty, I think it (the scoreline) should have been a lot more in terms of the chances we created.
“We’ve got to take our chances much better, but we’re really pleased with scoring three goals and keeping another clean sheet.”
The shutout was North End’s third in succession while the result made it back-to-back home wins.
“We’ve always said it’s not just about the defence when we keep a clean sheet, it’s about the whole team defending and we’re pleased with how the have team defended when we haven’t got the ball. That’s helped us get the ball back and create more chances so we’re really pleased with that.
“It’s not just about the results, it’s about how we play and what we’ve been pleased with is how we’ve actually played in those three games.
“We’ve passed the ball well, worked hard for each other and we’ve defended and attacked together as a team, so we’re just as pleased with the performance as we are with the result. But it’s always good to win games.”
The academy boss suggested that confidence is on the rise for his young side.
“I thought we played well, we passed it well, opened them up and wanted to get on the ball, and I think that’s what we’ve done for the last three games as well.
“We’ve looked like a team that’s full of confidence and that’s what you want, that’s when players play at their best.”
PNE line-up: Roberts; Creech, Stead, Lyons, Campbell (Walker, 61); O’Neil, Smart (Mason, 70); Howard (Wood, 46), Meulensteen, Earl; Garstang. Subs not used: Burgoyne, Lenton.