Fulham boss Martin Jol said: "For us, today was vital. You know you can get dragged into problems but now we have 32 points we can look forward to the next couple of games.
"I feel you always need special, professional players who can make a difference and today it was Dimitar.
"We were the better team in the first half but we needed Mark Schwarzer to get us the clean sheet and the three points."
The Dutchman believed Stoke midfielder Steven Nzonzi was fortunate to escape with only a yellow card for striking Bryan Ruiz after the Fulham player had released the ball.
Jol said: "I think he's very lucky to get a yellow card. This was a sort of knockout punch that was more than red. It was evil."
Stoke boss Tony Pulis said: "The first half was flat, the only real quality was Berbatov's great strike.
"In the second half we missed an opportunity, missed a penalty - that's been our story away from home. We haven't taken chances when games have been tight."