Potters striker Kenweyne Jones spurned the best chance of a tight first half when his header drifted wide of West Bromwich Albion’s goal.
The Baggies rarely threatened, and the visitors took the lead in the 74th minute after Michael Kightly’s good run and cross was tucked past West Brom goalkeeper Boaz Myhill by Whitehead.
“It’s undoubtedly a huge monkey off of our back, having finally picked up those three points here today,” said Pulis.
“We have had four draws away from home this year and in a couple of those, we have been hugely unfortunate not to have won the game.
“We have performed a lot better on the road this season, but we have just needed that little bit of luck on the day to get us over the finishing line. Thankfully today, things went our way and we got the win we were all so desperate for.”
He added: “We felt a win would come if we continued to do the same things as we have been doing, and hopefully this win can prove to be the springboard for us to go on and pick up more points on the road.”