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 minute, 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.
Source: PA
Source: PA