The hosts went 1-0 down in the 31st minute when their slack play at the back allowed Marouane Chamakh to score on his first Palace start.
Charlie Adam equalised in the 58th, dispatching a shot beyond Julian Speroni from Jon Walters' pass.
And Ryan Shawcross - who had been outmuscled by Chamakh in the build-up to the visitors' goal - then netted what proved to be the winner in the 62nd minute, firing in when the ball ricocheted his way in the area.
The result provided Hughes with his first points since being appointed as Stoke boss over the summer, and his first Barclays Premier League win since May 2012, when he was manager at QPR.
Both Stoke and Palace were looking to bounce back from 1-0 defeats on the opening weekend of the season, and it was the home side who started the contest most brightly.
Adam drilled a low shot from outside the box into the arms of Speroni in the sixth minute and the Potters continued to pressurise, winning three corners in quick succession but not being able to make anything of it.
Dwight Gayle tried his luck at the other end in the 16th minute with a strike that Asmir Begovic got down to save, and Palace fans then appealed for a penalty when Joel Ward went down in the area under the attentions of Matthew Etherington, but referee Andre Marriner judged there had been no foul committed.
Peter Crouch passed up an opportunity to put Stoke ahead in the 21st minute, nodding Etherington's cross over the bar from inside the six-yard box.
Palace had steadily been growing into the contest and just after the half-hour mark, they snatched the lead as Chamakh made the most of some poor Stoke defending.
Alongside Shawcross, Chamakh chased a long ball which had been lofted forward by Damien Delaney, shrugged off the Potters defender with relative ease, cut inside - fooling Robert Huth - and slammed a shot past Begovic.
The hosts almost found an immediate reply as Crouch rose to get his head to Adam's delivery and sent the ball against the bar.
Palace were soon back on the attack, though, with Dean Moxey flashing an effort across the face of goal and narrowly wide.
Jose Campana then looped a free-kick over the bar as the visitors finished the first half strongly.
Stoke began the second period looking intent on getting themselves back in the game and within two minutes of the restart another good chance was missed by Crouch, with the striker completely miscuing an attempted header from a corner.
Steven Nzonzi did not do much better in skewing a shot wide five minutes later, but Stoke kept up the tempo and Jon Walters' produced an improved effort, lifting the ball over the bar.
The equaliser duly arrived soon after as Walters received the ball from Crouch's header and laid it to Adam, who placed it past Speroni into the net.
Stoke's momentum then swiftly yielded another goal as Huth and Shawcross made amends for their earlier sloppiness.
Good perseverance in the box from the former saw the ball break for Shawcross to smash it home.
Jason Puncheon went close to scoring a quick leveller, bursting into the box and unleashing a strike which Begovic slowed with a finger-tip at full stretch before smothering.
Stoke then nearly added to their tally as Nzonzi lashed the ball against the post.
Palace remained full of belief and after substitute Kevin Phillips had shot wide, Gayle was off-target with an ambitious volleyed attempt.
Gayle also produced another unsuccessful shot in stoppage time as Stoke held on for the win.