Gary Megson's West Brom secured their first win of the season after a 47th minute goal from defender Darren Moore was enough to see them home.
The ball finally found its way into the net after Edwin van der Sar blocked Moore's initial effort from a Neil Clement corner.
However, controversy surrounded events leading up to the winning goal after Clement was ordered to retake his original corner after Rufus Brevett had intercepted his set-piece at the near post.
There appeared to be no clear reason for referee Rob Styles' decision. Nonetheless, Fulham could have no complaints over the goal itself.
Speaking after the match, Baggies boss Gary Megson was pleased with the win:
"It's nice to get the first win and the first clean sheet and the first points.
"It's taken a while coming. But we are playing the top teams in Europe and last year we lost 11 games in the First Division. It's a massive step-up. It's almost like a different sport."
Meanwhile, boss Jean Tigana was courteous in defeat.
He said: "West Brom played very well and had good organisation. They use the long ball and have two good strikers, but I'm disappointed we gave the goal away from a corner kick."