The former England striker scored the winning goal in the 70th minute at the Britannia Stadium as Stoke made it back-to-back home wins in the league with a 2-1 victory over Aston Villa.
Half-time substitute Charlie Adam had given the hosts the lead in the 51st minute before a poor header from Erik Pieters allowed Libor Kozak to level 15 minutes later.
Crouch has been linked with a move to join up with either of two former managers - Harry Redknapp at QPR or Tony Pulis at Crystal Palace - with Stoke reportedly chasing Hannover striker Mame Biram Diouf.
But Hughes said: "He's not going anywhere in January."
Crouch was named man of the match, and Hughes added: "He obviously gives us a focus to our attacking play.
"I played that role for many years with my back to the goal, and it's a thankless task on occasions. Sometimes you have to take hits for the team. That's what Peter did today and has done for a long time.
"He's an accomplished football player. He's being playing at this level for a long time and you don't do that unless you're a very good player."
It could be a red letter day for the Crouch family, with wife Abbey Clancy contesting the final of Strictly Come Dancing later.
Crouch told the BBC: "I'd like to think I've given her some tips but I've only got the robot in my locker."
Stoke have lost only one of their last eight Premier League games and the victory lifted them up to 10th place.
Hughes said: "It was a little bit difficult for us to get a foothold in the game in the first half. The wind was in our face and we didn't really get on the front foot and have that platform to build the performance.
"But I made a change at half-time and I think that probably helped us, and we were much better. We had the benefit of the wind at our back, which made an immediate impact.
"Obviously Charlie came on and scored, which settled the half very nicely for us, and we were very much on the front foot then.
"We had to pick ourselves up with the disappointment of the equaliser but I was really pleased with the reaction of Erik and his team-mates. They got round him, picked him up very quickly and that was important for us.
"And then we were able to go on and score a great goal at the other end. The second-half performance was very good."
Aston Villa have now lost three games in a row but manager Paul Lambert was encouraged by their performance, especially in the first half.
He said: "I never thought we deserved to lose that one. The last two performances against Fulham and Manchester United, we didn't deserve anything, but that one I thought we deserved something.
"We got ourselves back into the game in really strong condition. I couldn't fault the lads for their effort and the way we started. I thought we were the better team in the first half. We looked threatening. I'm disappointed to lose but that was better from us."
Lambert left out striker Christian Benteke, who has been struggling with a knee problem, and confirmed the Belgian is a major doubt for the Boxing Day clash with Crystal Palace.
"He's been carrying the injury so we'll just have to try to get it right," said Lambert. "Hopefully the rest will do him the world of good. There's too many games to risk him."
Lambert, meanwhile, did not have too many complaints about referee Craig Pawson's decision only to show Marc Wilson a yellow card during the first half.
A mistake from the Stoke defender allowed Andreas Weimann through on goal but Pawson deemed the striker had played the ball too close to keeper Asmir Begovic before Wilson brought him down.
Lambert said: "Andi's got there first but the referee's interpretation was that the goalkeeper had possession of the ball and we have to respect his decision.
"Some referees might have been different. We understand that he didn't think it was worthy of a red card."