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.
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.
"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.
"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."
Cottagers captain Danny Murphy - who specifically mentioned Stoke last season when speaking about teams being sent out too "pumped up" and to stop other sides playing by their managers - was booed every time he touched by the ball by the Potters fans.
It is an issue Pulis is keen to move on from, although he admitted it had helped to keep the atmosphere lively whenever the tempo dropped on the pitch.
"That is the way it is - that is the life in sport and you have to accept that," Pulis said of Murphy's reception.
"It was good for us because there were spells in the game when it went a bit quiet, and it certainly livened it up."
Fulham boss Martin Jol was disappointed to see his team's defence breached with only 10 minutes remaining.
"We always knew that they are capable of scoring a goal with their strength, and that is exactly what they did," Jol said.
"We talked about it - it is not enough only to be on the end of the first ball, you have to win the second balls as well, because that is what they do.
"There was nobody at the edge of the box for Etherington's shot (when Walters scored) and that was pretty frustrating.
"I think we are a solid team at the back. It is not easy, and there are a lot of teams who have problems here and I don't think we had a big problem.
"But if you are hoping for a 0-0, you have to do your bit for 90 minutes, not 80 minutes."