The Dutch left-back scored for the first time in six years when attempting a cross late in the first half, which was misjudged by Tim Krul and allowed to drop in off the post.
The win, which extends Stoke's unbeaten run at home to six games, brings them to within three points of Alan Pardew's side, heaping more pressure on the Magpies boss.
Despite a comfortable mid-table position, recent poor performances have left Pardew's future shrouded in uncertainty, with unrest growing among their supporters.
|By Simon Harrison
There were loud chants of "we want Pardew out" from the Toon support at the end of the game, with banners to match. The away fans are not happy with their side's performance and they have got every right to feel that way.
There were not enough standout showings from the Magpies on Saturday, with their experimental system not achieving what their manager desired.
A toothless Toon were trumped by a fluke goal from Erik Pieters but Stoke won't care one bit. Marko Arnautovic was the star of this show, with Newcastle unable to rustle up a contingency plan to keep tabs on the Austrian forward, who ran riot.
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 scraping 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, though neither could hit the target.
Stoke were rewarded for their efforts three minutes before the break in unlikely circumstances as Pieters's 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.