Papiss Cisse scored early in the second half for the visitors, but Stoke battled back to level through Jonathan Walters before Cameron Jerome swept home the winner with five minutes remaining.
"Their goal gave them a lift but they are still a good side. Although they have players missing they are still a good side and it is a great victory for us, we showed great character," he said.
"We missed a couple of really good opportunities to go in front and when they score you have to show a lot of character to get back in the game and then go on and win it."
Pulis brought on goal hero Jerome, who also created Walters's equaliser, just after the hour and he believes his introduction along with that of Michael Kightly changed the game.
"For 15 to 20 minutes they looked very comfortable and then we made the changes with Kights and Cameron Jerome and that changed the game.
"They livened it up for us. Cameron and Michael came on, they gave us pace and livened us up and if you look at the chances we missed it certainly pushed them back and gave us opportunities to score."
Pulis was particularly pleased with Jerome's winner, adding: "It was lovely for him to score, he has been great around the place. Him and Kenwyne Jones have been very frustrated that they have not played and I understand that but the two of them have come on and really shown their class and I was really pleased for them and Michael too."
The Stoke boss admits he is pleased that their form has picked up in recent weeks.
"10 from 12, we will take it whether we are winning or losing, we are pleased to be on a good run but nobody will get carried away," he added.
He also gave an update on Peter Crouch's injury as he was forced off early on after being caught by a stray arm from Fabricio Coloccini.
"The doctor had couple of teeth in his hand when he walked off and he has one or two right in his gum too so he is going to have to have a little bit of work done on his teeth," he confirmed.