Gareth McAuley struck a last minute header to secure Albion a point at Craven Cottage – netting the Baggies' first goal of the season in the process.
The centre back, who scored twice on international duty, rose highest to convert Chris Brunt's corner in stoppage time after Steve Sidwell had given the hosts a first half lead.
Fulham were without Darren Bent, Aaron Hughes and Maarten Stekelenburg going into the game, with Adel Taarabt also not fit enough to start. Kieron Richardson faced his former club.
Albion were without Ben Foster and Shane Long, while Stephane Sessegnon awaited his work permit. Victor Anichebe and Morgan Amalfitano were handed full debuts.
The home side, usually so effective at their West London home, enjoyed more of the possession in the opening stages. But Ruiz failed to trouble Myhill from distance, while Olsson had to stoop to prevent Kasami from latching onto a Berbatov through ball.
Brunt, returning to the starting XI, nearly caught out Stockdale with a vicious swinging shot, before the hosts took a scrappy lead. Sidwell, who alongside Parker in the middle of the pitch was very busy, aimed the loose ball from a corner towards goal, and although Myhill reached it, he could only palm the shot into the net.
Brunt again attempted to unnerve Stockdale with a curling free kick that caught everybody out but his speculative effort spun just wide of the post. Amalfitano looked lively, demonstrating his ability to deliver a ball from the flank, while Anichebe was battling hard against the intimidating Hangeland and Senderos, without reward.
Anelka was finding it difficult to stamp his authority on the game, as was Fulham's luxurious equivalent in Berbatov. The Bulgarian, however, did have the ball in the net, only to see the offside flag rule it out.
Albion's best move was started and very nearly finished by Billy Jones. He played in to Anichebe, who held up the ball before laying it off to Amalfitano. The Frenchman crossed towards the right back who'd continued his run, but Senderos was there to deny him.
It was certainly Fulham's half.
After the break
The visitors looked livelier at the beginning of the second period. Although Berbatov had the ball in the net only for the flag to go up (again). Anichebe had Albion's first real clear cut chance of the match. The Nigerian kept Hangeland at bay on the turn, but his low shot was held by Stockdale, who breathed a sigh relief.
Berbatov was coming more and more into the game – a danger for Albion. He was denied by Myhill after poor defending, before his excellently executed bicycle effort flew just over the bar.
A flurry of changes then came. Richardson, who has barely played in the last few months, was replaced by Amorebieta, while Rodallega replaced Berbatov. Steve Clarke took off Amalfitano and the quiet Yacob, giving Morrison and Sinclair run-outs in the hope of nicking a result.
Anelka had an excellent chance when in on goal, only to lose control of the ball. It hadn't been the Frenchman's day – although he was clipped as he tried to rescue his poor touch. Berahino came on for the hardworking Anichebe.
The Cottagers had an excellent chance to kill the game off when Ruiz was allowed too much time on the edge of the area, but his thumping strike came back from the underside of the crossbar. Sidwell's rebound was the third goal of the day for the home side to be disallowed.
The Costa Rican soon required a substitution, after falling awkwardly. Damien Duff replaced him.
Albion pushed and pushed for an equaliser. Morrison and Mulumbu very impressive, while Kacaniklic enjoyed a fruitful afternoon on the wing for the Whites.
As six minutes of injury time was signalled, McAuley rose above the Fulham defence to meet a Brunt corner and aim it past the helpless Stockdale. The away end fell into raptures, understandably, after having little to shout about so far this season.
Match ratings
FFC: Stockdale 6; Riether 7, Hangeland 7, Senderos 6, Richardson 7 (Amorebieta 5); Parker 6, Sidwell 7, Kacaniklic 7, Kasami 6; Berbatov 6 (Rodallega 5), Ruiz 6 (Duff 5).
WBA: Myhill 6; Jones 6, McAuley 7, Olsson 6, Ridgewell 5; Yacob 5 (Morrison 6), Mulumbu 8, Brunt 7, Amaliftano 6 (Sinclair 5); Anelka 5, Anichebe 6 (Berahino 5).
Have your say on Albion's draw here at Baggies Banter.