The £8million record signing struck for the first time since November with a powerful header that opened the scoring in a hard-fought Barclays Premier League win at the Britannia Stadium. Everton had a number of opportunities to equalise before Stoke's victory was secured by a Phil Jagielka own goal in the second half.
Pulis said: "Kenwyne has done smashing. Although his performances may have dipped a little bit, we have great belief in him. Playing with two wingers suits him and his goal was a fantastic header."
He added: "There were a few moans and groans but you get that at most grounds. They were brilliant with him today, I'm so pleased for him. Kenwyne has had an issue off the field which I don't want to go into, it's a family thing. He's a loving kid and a good kid.
"It might have affected him a little bit but we have dealt with it the way we do. I've put no pressure on him and let him do it. I was very pleased with the goal today and I think that gave him the confidence to play as well as he did."
Opposite number David Moyes had no doubt referee Andre Marriner should have given a penalty in the first minute when Ryan Shawcross appeared to kick Louis Saha on the edge of the area.
Moyes said: "If it's not a penalty it's a free-kick, one or the other. He catches him in the midriff. You tell your players to play to the whistle, right until the last minute of the game.
"The rules have got to apply to the referee. From the first second he has got to be ready to blow his whistle and I don't think he was quite ready."
Moyes added: "I don't think the score justified the result. I thought we played well enough to get something out of the game.
"We played really well in the first half but found ourselves 1-0 down. We didn't do so well in the second half but I don't think the score was the correct score."