The Potters fell behind in the 31st minute when Ryan Shawcross was beaten to a long ball by Marouane Chamakh, who cut inside Robert Huth and fired past Asmir Begovic.
But the hosts fought back with two goals in quick succession after the break, Charlie Adam slotting in the first in the 58th minute and Shawcross smashing home the second four minutes later.
With Stoke having lost their Barclays Premier League campaign-opener 1-0 at Liverpool last weekend, this result brought Hughes - appointed as the Staffordshire outfit's manager over the summer - not only a winning start at home, but his first points in the job.
And following the victory, Hughes said: "Premier League points are like gold dust and this was important for us - I'm a new manager working really hard with a new group of players.
"In fairness to them, they have worked their socks off to try to implement what we are trying to do.
"We will get better - we weren't great today and we can play better, and we I think we all accept that. But the important thing today was to get a positive result."
Giving his assessment of the contest, Hughes said: "We were a little bit apprehensive in the first half. Credit to Palace, they pegged us back.
"It was a little bit difficult with the wind in our face to get out of our own half in that first half, and we were a little bit too respectful of Palace and didn't get close enough to them.
"They were able to put passes in between the lines and that caused us a problem initially, although they didn't create too many chances - we created one for them, which was uncharacteristic from Ryan.
"At 1-0 down, we needed to do something. We needed to be more on the front foot and ask more questions of Palace, and I thought we did that in the second half.
"I thought we were much more dynamic, got to the ball better and quicker, and as a consequence we got back in the game.
"It was a great finish by Charlie - he didn't have a lot of time to understand the situation he found himself in but dispatched it with a really great finish.
"And Ryan then made amends for his mistake, showing great determination and getting his rewards."
The ball broke to Shawcross in the box for his goal via a coming-together between Huth and Chamakh as the visitors struggled to clear.
Chamakh, making his first Palace start, was substituted almost immediately afterwards.
But asked if that had been as a consequence of the striker's failure to make a stronger challenge, Palace manager Ian Holloway said: "Not at all, no. He did his best to get there. Where were my defenders?"
Holloway - whose newly-promoted side also lost their opening game of the season, getting beaten 1-0 at home by Tottenham - felt there had been plenty of encouraging signs from his men over the course of the Stoke contest, but was disappointed they had been unable to prevent the Potters' two goals.
He also criticised Palace fans for a song they had sung about Hughes.
"There was a little spell in the game where Stoke scored a couple of goals and we couldn't get back in it," Holloway said.
"But I thought it was a better performance than last weekend, and I thought the new lads particularly helped the group.
"Chamakh's goal was very pleasing - I know he can score goals and I think he proved he wants to there.
"But what we have to do is work as hard as we did in the first half all the way throughout the game. Unfortunately the fitness levels showed a little bit.
"We tired, and Stoke got on with it - even with our crowd singing stupid, ridiculous things, which I hate. That is all you need to get spurred up.
"It was tight and close and I was quite pleased with certain things.
"But with the first (Stoke) goal, I felt we got it wrong as a group - we didn't get organised.
"Then for the second one, Chamakh tried to toe-punt it out, they made a tackle and it has rolled straight to them.
"When you look at those goals, I am disappointed because we played better than that, but that is this level."
Asked about the Palace supporters, Holloway added: "They were wonderful, but no-one should ever sing about a manager getting sacked in the morning - I don't find that particularly funny."