SUPER-SUB Somen Tchoyi picked the perfect moment to bag his first goal of the season - with his 82nd-minute leveller earning Albion their first-ever Barclays Premier League point at Craven Cottage.
The Baggies had just about shaded this tight encounter in West London but fell behind when in-form Fulham striker Clint Dempsey coolly slotted home his 16th of the season in the 70th minute.
Albion, however, weren't to be denied a precious point and Tchoyi's well-taken goal made it just one defeat in six on the road.
It was a night of reunions as Cottagers boss Martin Jol faced the club he served for a couple of years in the early 80s while Roy Hodgson made his first competitive return to Fulham since joining Liverpool in the summer of 2008.
Hodgson's two-and-a-half-year reign on the banks of the Thames was fairytale stuff and his reception from the home fans as he walked across the pitch to take his place in the away dugout was in complete contrast to the sub-zero temperatures in the capital.
At kick-off, it was 14th entertaining 15th, with the teams separated by a single point.
Peter Odemwingie was recalled to the starting line-up - replacing the injured Jerome Thomas - in Hodgson's only change from the club's last league game at Stoke 11 days ago.
Albion were also without Paul Scharner, Shane Long and Billy Jones while deadline-day signings Liam Ridgewell and Keith Andrews were ineligible.
Their absence gave another January capture, Scott Allan, his first involvement in a matchday squad while teenager Sam Mantom and fit-again Steven Reid were also among the subs.
Jol also made one league change as Simon Davies replaced Bobby Zamora, who joined QPR yesterday.
The match clock ticked into the third minute when Fulham recorded the first shot of the game, with Steve Sidwell shooting well wide from 25 yards after neat build-up play by the hosts.
Simon Cox was equally ineffective with an effort from similar distance three minutes later which dribbled past the right-hand post.
The pattern of long-range efforts continued and, in the eighth minute, David Stockdale had to dive low to his right to clutch an awkward bouncing shot from James Morrison.
Albion had started well and they could have been 1-0 up on 13. A slick move involving Graham Dorrans and Cox resulted in the latter putting Odemwingie in the clear, but from a tight angle, the Nigeria striker shot horribly wide from 15 yards.
Fulham got on top for a short period and won a couple of corners, but they were comfortably repelled by the Baggies rearguard.
There was a little more concern when Sidwell was allowed to advance and shoot, but like his earlier effort, he failed to trouble Ben Foster's goal from 25 yards.
On 23, Albion broke superbly from the back and Cox set up Dorrans in the box with another perfectly-placed pass. The Scottish international took aim but saw his effort deflected wide by Brede Hangeland.
The action swung straight upfield and former Fulham loanee Nicky Shorey and skipper Jonas Olsson made important blocks in the penalty area in quick succession to deny Sidwell and Danny Murphy respectively.
But it was Albion who almost took the lead again on 25.
Odemwingie pulled the ball back to Marc-Antoine Fortune who dummied Phillipe Senderos before seeing his low 15-yard effort pushed wide by Stockdale at full stretch.
Foster has been in great form of late but had a slice of fortune when, in rushing to the edge of his area, he was beaten to Murphy's lofted ball by Bryan Ruiz. Thankfully for the Albion No.1, the Costa Rican's header bounced well wide of the empty net.
Another great Cox pass, this time down the right, found Odemwingie and, despite losing his footing, the former Lille man was able to nudge the ball back to Fortune, who blasted over from 18 yards.
Fulham forward Dempsey, who scored a hat-trick in his last league game, was the next player to try his luck from range, but he shot well wide from 25 yards.
After a lull in the action, Dempsey was much accurate on 44, but Foster comfortably gathered the American's 18-yard grass-cutter in front of his left-hand post.
After the restart, the lively Cox warmed up Stockdale's hands with a fierce 25-yarder which flew straight at the Fulham keeper.
Albion had been the better side in the first 45 and they continued to look the team most likely after the break.
Odemwingie did brilliantly to outmuscle Hangeland in the Fulham box before cutting the ball back to Fortune who spun sharply before seeing his angled shot stopped, and then gathered, by Stockdale.
Moments later, Ruiz had the Baggies defence back-pedalling and after skipping past Morrison and Olsson, the Fulham forward stabbed straight at Foster from 15 yards.
John Arne Riise then advanced towards the Albion box before screwing a shot just wide from 20 yards.
Fulham were enjoying their most dangerous spell of the game and Damien Duff cut in from the right and fizzed a cross-cum-shot across the face of goal.
Back came Albion and from Shorey's dink, Odemwingie saw his goalbound shot from inside the box blocked by Sidwell.
But the Baggies fell behind with 20 minutes left.
Dorrans miscued an attempted clearance across the edge of his own penalty area and Sidwell and Ruiz combined to thread in Dempsey, who gave Foster no chance with a shot on the turn from 12 yards.
Albion regrouped and put the Cottagers' goal under sustained pressure by winning a string of corners.
And they got their just desserts when Tchoyi, who had been on the field just five minutes, raced onto Morrison's neat lay-off before firing in off Stockdale from a tight angle.
Had Albion showed a little more composure during the latter stages, they may even have made it four away wins in five, but they were also relieved to see Riise plant a late free-kick into their defensive wall.
FULHAM (4-4-2): Stockdale; Kelly, Hangeland, Senderos, Riise; Davies, Murphy, Sidwell, Duff; Ruiz, Dempsey. Subs not used: Etheridge (gk), Hughes, Baird, Kasami, Gecov, Frei, Trotta.
ALBION (4-4-2): Foster; Tamas, McAuley, Olsson, Shorey; Cox (Tchoyi 77), Morrison (Reid 88), Mulumbu, Dorrans; Odemwingie, Fortune. Subs not used: Fulop (gk), Mantom, Dawson, Thorne, Allan.
GOALS: FULHAM - Dempsey (70). ALBION - Tchoyi (82).
BOOKINGS: FULHAM - Murphy (foul 51).
REFEREE: M Halsey (Lancashire).
ALBION STARMAN: Youssouf Mulumbu.