Martin Jol's side have struggled for consistency this season and were without a win in their last four games heading to The Hawthorns, but produced a spirited display to edge their hosts through Alexander Kacaniklic's winner.
A drab second half saw the visitors stun home fans by taking a 39th-minute lead, when excellent work from emerging winger Ashkan Dejagah was converted clinically by talisman Dimitar Berbatov.
The Baggies came out for the second period with Steve Clarke's words ringing in their ears and quickly squared the match with a close-range finish from Romelu Lukaka, who had been superbly located by the marauding Billy Jones.
But two minutes short of the hour, the game swung decisively - Bryan Ruiz's speculative long pass chased down by Kacaniklic, who spun in between two West Brom defenders before shooting through the legs of Ben Foster from 18 yards.
Sky Sports pundit Alan Smith was impressed by Fulham's resilience given the momentum gained by West Brom, and says the west Londoners can now look upwards again in terms of the table.
He said: "They looked like a team today having looked a bit disjoined of late and making some silly mistakes. They had to dig in today in the second half when West Brom came at them.
"I think the away team dressing room at The Hawthorns will be buzzing right now. It could be a turning point for them because they've got Wigan and West Ham in their next two home games at Craven Cottage. If they can get back to being strong at home, then they can start climbing the table.
"Berbatov was never going to panic when he had the chance. He just gives a side a different dimension. He would have lifted everybody in that side because any player wants to see that kind of quality coming into the club - even if it's in your position. It raises everybody's game.
"I think on another day, West Brom might have had two or three. If you look at the second half, they were a little unlucky. Fulham hung on to a certain extent. It was a good response from the home team and they'll want to focus on that.
"Steve Clarke will still be pleased a little over the half-way mark of the season. I'm sure he'll change things a bit for the FA Cup match they have coming up and they'll try and go again in the New Year."
Fellow presenter Matt Le Tissier was similarly taken by the battling qualities of Jol's side and had glowing words for the composure shown by Kacaniklic in netting the winning goal.
He told Sky Sports: "You thought, with getting the equaliser so soon after the break that West Brom would go on and win the game, but Fulham showed a great deal of character.
"I thought Billy Jones did very well - especially in the second half. When he set up the equaliser for Romelu Lukaku, he looked more like a tricky winger than a full-back.
"For the winner, Kacaniklic's first touch was brilliant. He took a lovely first touch, just checked back and passed it through the defender's legs. The defending could have been a little bit tighter but it was a lovely bit of skill.
"It's a difficult place to go and play but I thought that they deserved to go in at half-time leading. It wasn't a great first half, but Fulham kept the ball better.
"In the end, three points could be pretty crucial when you see the tally they were on before this game. They were just looking over their shoulders a bit towards that bottom three places."