The hosts hit the post through Rory Delap and saw their own crossbar rattled by John Arne Riise before Jon Walters broke the deadlock in the 80th minute, diverting Matthew Etherington's effort home. Delap then doubled their advantage seven minutes later, nodding in an Etherington free-kick.
"It has been a great start to the season and we are very, very pleased," Pulis said. "But we know in football that it can change so, so quickly and we will just keep our feet on the ground and the players will keep working hard."
The deserved win means the Staffordshire outfit have 12 points from their opening eight Barclays Premier League fixtures this term and sit in seventh place in the table.
They are also top of their Europa League group and through to the Carling Cup fourth round, having been beaten only twice in 15 games in all competitions.
Pulis is delighted with his team's progress but remains wary of complacency.
He added: "We want the supporters to enjoy this period and really get behind the lads, and they have been doing that, so it is smashing at the moment. But if you take your eye off the ball in this game, then it can soon fall and crumble away."
After a sluggish start, Stoke exerted increasing pressure on their opponents and Riise's free-kick against the woodwork was the only real moment where Fulham threatened in the second half.
"It was a good three points," Pulis said. "They are a good side and I thought we contained them very well today in free play. They looked more dangerous off throw-ins and free-kicks, and Riise's effort in the second half was inches away from giving them the lead.
"But in general play, I thought we really contained them very well. Maybe on another day if we had had a little bit more luck and things had run for us, we might have scored more goals."
Source: PA
Source: PA