Second-half goals from Robert Huth and Cameron Jerome put the Potters firmly on course for the three points but the Royals threatened another late comeback when Adrian Mariappa pulled a goal back with seven minutes remaining.
However, Stoke managed to stand firm although there was a nervy moment late on when referee Michael Oliver waved away Adam Le Fondre's penalty appeals.
Pulis said: "It has been a long time. I thought we deserved to win the game - I would have been absolutely devastated if we hadn't won the game today.
"After the first half I thought we deserved to be coming in leading, but we just picked the pace up and the two subs (Jerome and Kenwyne Jones) made a great difference again.
"Cameron Jerome is a great impact player and he scored a great goal."
Regarding the Le Fondre incident - when the striker went down in the box under a challenge from Ryan Shotton - Pulis said: "I haven't seen it on television.
"Firstly I was told it was a penalty, then I've just been told (you can see) it actually isn't from a different angle - that the lad isn't caught, but just arches his back and falls over.
"It will be interesting to see, but if it was a penalty, I have to say thank goodness we have had a break, because we deserve one."