The Dutchman found the net when his over-hit cross from edge of area looped over the head of the stranded Tim Krul just before the break.
Peter Crouch should have extended the lead, spurning a flurry of headed chances, while Dan Gosling wasted Newcastle's best opening early on.
The result continues Stoke's impressive run at home, where they are now six unbeaten, while heaping more pressure on Newcastle manager Alan Pardew.
Despite a comfortable mid-table position, recent poor performances have left Pardew's future shrouded in uncertainty, with unrest growing among their supporters.
Newcastle came into Saturday's game in wretched form, having conceded 11 goals in a run of three consecutive defeats.
It is a far cry from the position they found themselves in after a 5-1 victory over Mark Hughes' side in December, when Newcastle moved up to sixth and just three points adrift of a UEFA Champions League berth.
And Pardew's men were almost behind inside 10 minutes at the Britannia Stadium. A teasing cross from Marko Arnautovic found Crouch inside the six-yard box but the striker's header hit the post.
Much had been made about the absence of Loic Remy beforehand, with Newcastle only managing one league goal without the Frenchman in their side this season.
However, the visitors were handed a golden chance to improve on that record two minutes later, when a Shola Ameobi flick-on found Gosling inside the area, only for the former Everton man to divert his effort over the bar.
Newcastle began to look more comfortable in possession, with both Ameobi and Papiss Cisse causing problems.
But the hosts responded after 26 minutes, when the lively Arnautovic teed up Steven N'Zonzi and then Peter Odemwingie two minutes later, but neither could hit the target.
And Stoke were rewarded for their efforts three minutes before the break in unlikely circumstances as Pieters' lofted cross from the left eluded everyone, floating over the head of international team-mate Krul and into the top corner of the net.
Arnautovic continued to provide a threat to the visitors and found Crouch again just after half-time, only for the towering striker to loop his header over the bar.
Crouch had another great opportunity just after the hour, getting ahead of Mike Williamson before heading Geoff Cameron's cross straight at Krul.
Adam Armstrong and Hatem Ben Arfa were thrown on for the visitors as they looked to unlock a resolute home defence, but Stoke remained the better side.
Arnautovic raced away once again down the left 15 minutes from time, before squaring to substitute Charlie Adam, who skewed his shot wide.
Vurnon Anita headed over for Newcastle late on after some good work from Ameobi as the visitors searched for an equaliser, but Stoke held on to move to within three points of Pardew's charges.
