Both sides had glorious chances to break the deadlock in the first-half, with Stoke's Peter Crouch heading against the post whilst Dan Gosling scooped over a great chance from six yards out.
But it was the Potters' full back Pieters, one-time target of Newcastle, who opened the scoring just before half-time when his mishit cross got caught in the wind and looped over fellow countryman Tim Krul, and into the net.
Newcastle had chances to equalise through Mike Williamson's close range shot and Vurnon Anita's late header, but Stoke's defence remained firm throughout.
The Potters could have easily doubled their lead, with Charlie Adam and the superb Marko Arnautovic failing to convert their second half chances - but it mattered not, with Stoke holding on for a win that closes the gap on 9th placed Newcastle by three points.
The visitors were boosted by the return of goalkeeper Tim Krul from injury while Stoke captain Ryan Shawcross became the first player to make 200 Premier League appearances for the club.
The hosts, watched by their biggest crowd of the season, have lost just twice at the Britannia Stadium in the league all campaign and they should have taken the lead in the 10th minute.
The dangerous Marko Arnautovic swung over a perfect cross but leading scorer Peter Crouch headed against a post from five yards.
Two minutes later it was Newcastle's turn to miss a golden chance as Shola Amoebi's flick found Dan Gosling in front of goal six yards out but he could only slice the ball over the bar.
Most of the pressure was coming from Stoke but Ameobi and his strike partner Papiss Cisse were causing problems for the hosts.
The latter wanted a penalty after going down under a clumsy challenge from Geoff Cameron but referee Mike Jones was unmoved.
Steven Nzonzi tried his luck at the other end in the 26th minute with a shot from the edge of the box that was deflected over the bar by Fabricio Coloccini.
Peter Odemwingie had a similar opening soon after when he was well found by Arnautovic but he miscued his shot horribly.
Then in the 42nd minute Stoke made the breakthrough, Pieters floating his cross just beyond the despairing reach of Krul.
It was undoubtedly tough on Newcastle, who tried to respond before the break through Cheick Tiote but his fierce long-ranger was well held by Asmir Begovic.
Like the first half, the first chance of the second period was a Crouch header from Arnautovic's cross, but this time the striker could not quite get over the top of the ball.
And Crouch threatened again in the 61st minute, this time with a header from Geoff Cameron's deep cross, but Krul was behind it.
Shawcross showed his value at the other end with a block from Mike Williamson's goal-bound shot, leaving the Newcastle defender with head in hands.
Charlie Adam entered the fray as a 66th-minute replacement for Ireland and wearing a mask to protect his nose, which he broke in four places in training this week.
The Scot is due to have an operation on Monday but did not want to miss the game.
And he almost made the game safe when he ran onto Arnautovic's clever pass but pulled his shot past the far post.
Begovic had been largely untroubled in the second half but Vurnon Anita spurned a great chance to equalise five minutes from time when he headed Ameobi's cross over an empty goal.
Boos from the travelling fans greeted the final whistle, with a 'Pardew Out' banner displayed.
Newcastle have taken just 13 points from 16 games since beating nine-man Stoke at St James' Park on Boxing Day.