It looked like the Magpies might claim a much-needed first away win when Papiss Cisse put them ahead two minutes into the second half.
The visitors held out until the 81st minute when Walters headed in the equaliser, and four minutes later they were behind as substitute Jerome tucked the ball under Tim Krul for the winner.
Steven Taylor was the latest Newcastle casualty on Sunday with a hamstring injury that could keep him out until February but captain Fabricio Coloccini did return after serving a three-match ban.
The visitors began quite brightly and had the first shot of the match after five minutes but James Perch's effort was five yards wide of Asmir Begovic's goal.
The Britannia Stadium had only witnessed six goals in six games this season prior to tonight, with Stoke conceding just once.
It was perhaps not surprising, then, that chances were at a premium in the early stages, although Stoke did almost take the lead in bizarre circumstances in the 16th minute.
Mike Williamson looked to have Glenn Whelan's free-kick covered but the Toon centre-back miscued his clearance and was relieved to see the ball rebound off the post.
From the resulting corner, Walters headed straight at Krul, while just before the half-hour mark Whelan's 25-yard volley almost found the top corner.
Stoke were looking marginally the more threatening and they may well have opened the scoring in the 33rd minute had Matty Etherington not overhit his ball to Charlie Adam, who would have only had Krul to beat.
Fulham boss Martin Jol described Stoke as bullies after the Potters' 1-0 win on Saturday but it was the home side who were in the wars tonight.
Geoff Cameron needed an early change of shirts after a clash drew blood but he was at least able to continue, unlike Peter Crouch, who was replaced by Kenwyne Jones five minutes before half-time.
The striker was caught in the mouth by a flailing arm from Coloccini and looked to have lost at least one tooth before he was led down the tunnel, still bleeding from the mouth, by Stoke's physio.
The first half had certainly not been action-packed but it took less then two minutes of the second for Newcastle to break the deadlock.
A long-range shot from Demba Ba, who almost joined Stoke in January 2011, was spilled by Asmir Begovic and Cisse followed up for his fourth of the season.
It was a much-needed goal for the Senegal international, who has struggled to find anything like his form of last season, but it was certainly a preventable one from Stoke's point of view after Whelan was robbed in midfield.
The Potters looked to respond quickly and Adam's cross found the head of Walters at the back post but he was under pressure and could only nod wide.
The home fans' frustration was growing and Cisse might have made it two in the 63rd minute but Begovic pushed away his shot, while at the other end Krul could not hold Walters' stinging effort and the striker blazed the loose ball well over the bar.
Stoke boss Tony Pulis made his final two changes, sending on Michael Kightly and Jerome for Adam and Etherington.
Begovic was called on again in the 77th minute when Cameron's attempted clearance hit Cisse and turned into a through ball for Ba, the keeper stopping the well-struck shot with his leg.
Stoke really should have been level shortly after, though, as Kightly hung up a lovely ball for Jones six yards out but he headed straight at Krul.
The home fans did not have long to wait as, in the 81st minute, Jerome swung over an inviting cross and Walters showed Jones how it should be done with a lovely header into the far corner.
And it was to get even better for the Potters three minutes later. Jones made amends for his miss by getting on the end of a long ball and squaring for Jerome to slide his shot under Krul.
The Britannia Stadium cheered loudly and as the final whistle blew Stoke were able to celebrate climbing into the top 10 while Newcastle remain only two points above the relegation zone.