Browne fired home the opener with 20 minutes gone, after a superb bit of skill on the edge of the penalty area to give him room to shoot and then Potts secured the points with a fantastic breakaway goal, threaded free by Maguire.
Declan Rudd also saved a late penalty from Sam Clucas to preserve the clean sheet in front of a vocal away following.
Manager Alex Neil had the luxury of naming an unchanged team from the one that thrashed QPR the previous week, but whilst it was the same personnel, the formation was tweaked, with Paul Gallagher playing in a deeper role.
And it was the North End skipper who had the first chance, three minutes in, as he collected a loose ball 25 yards out and drilled a low curler that England goalkeeper Jack Butland did well to get down low to his left to push behind for a corner – former Stoke man Gally being booed as he went across to take it.
A quarter of an hour in Browne almost capitalised on a short back pass by the home side’s own captain, Ryan Shawcross, but Butland came to the rescue of the Potters’ No.17, racing out and just beating the Irishman to the ball.
However, the PNE No.8 wasn’t to be denied on 20 minutes. A brilliant run from Darnell Fisher down the right, saw the full back check inside City's left back and saw a shot blocked, it fell to Browne, who superbly switched from right to left foot with a Cruyff turn, and drilled the ball past Butland into the bottom right hand corner for his tenth of the season.
Ben Davies, on 53 minutes, made a superb block on the line to deny Clucas from levelling up, after Bruno Martins Indi’s miss-hit shot from the edge of the box found the midfielder in the right corner of the six-yard box unmarked, but the centre half made a last-ditch block to keep the ball out.
After some good build-up play, on the hour mark, Browne saw a shot blocked on the edge of the box by Ashley Williams for another Gallagher corner, which brought a second, but despite a good ball in, Stoke managed to smother the ball away.
Brilliant play by Maguire at the mid-point of the second period saw him get away from Williams on the right and reverse the ball back towards Potts, only for Shawcross to make a vital interception and put the ball behind with the recent acquisition waiting to put the ball into the net.
Maguire then hit the post from Hughes’ pull back after a pacey counter-attack by Potts and substitute Barkhuizen – on for Stockley – the ball pulled back from the left byline to the Irishman, who deflected goalwards, with Butland beaten, but the ball came back of the left-hand upright and Gallagher’s shot on the rebound was blocked by Shawcross.
Hughes at the other end had to make a tremendous block to deny Clucas after some good play by Joe Allen and home substitute James McClean, who worked space on the left and then pulled the ball back to the former Hull City and Swansea man on the edge of the box with just under a quarter of an hour to go.
An almighty scramble, after the introduction of Peter Crouch, saw North End somehow keep it out, again via Hughes, and then on the break they made it two.
Ben Pearson was superb on the break, taking the ball from half way inside his own half, down the right-hand side, before finding Maguire, who saw Potts breaking down the middle unmarked; he kept his cool before sliding the ball past Butland into the bottom left hand corner of the goal in front of the buoyant 2,041 PNE fans.
With 30 seconds to go the home side were presented with a lifeline as Potts brought down Peter Etebo in the penalty area, but Rudd made a truly outstanding save to deny Clucas, diving to his left to push the ball onto the bar and Davies heading behind from the follow up and after five minutes of stoppage time the whistle followed as the Lilywhites made it back-to-back away wins.
Stoke City line-up: Butland, Bauer, Allen, Williams, Etebo, Afobe (Crouch, 79), Tymon (Sorensen, 43), Martins Indi, Shawcross (c), Clucas, Campbell (McClean, 61). Subs not used: Federici, Ince, Bojan, Edwards.
PNE line-up: Rudd, Fisher, Hughes, Pearson, Storey, Davies, Potts, Gallagher (c) (Johnson, 74), Stockley (Barkhuizen, 58), Browne, Maguire (Nmecha, 81). Subs not used: Ripley, Earl, Ledson, Huntington.
Attendance: 25,053 (2,041 PNE fans)
Referee: Mr O Langford