GARETH McAuley ended Albion’s goal drought in the second minute of stoppage time to earn the visitors a more-than-deserved point.
McAuley made it three goals in just over a week when he headed home Chris Brunt’s corner after scoring in both of Northern Ireland’s internationals against Portugal and Luxembourg.
Steve Sidwell’s first-half strike had appeared to sentence Albion to a harsh defeat on the banks of the Thames.
With nothing to choose between the sides, Sidwell broke the deadlock with a 12-yard volley from a 22nd-minute corner.
But the Baggies were much-improved from their home defeat by Swansea 13 days earlier, with debut boy Morgan Amalfitano’s delivery from the right causing Fulham plenty of problems.
And they created enough chances after the break, with new signing Victor Anichebe and Nicolas Anelka both being denied by David Stockdale.
Bryan Ruiz also hit the bar late on for Fulham before McAuley had the final say with Albion’s first league goal of the season.
Seventeenth entertained 20th as the clubs squared up for their fourth league game of the new campaign.
Deadline-day signings Amalfitano and Anichebe were handed their Baggies debuts as Clarke made three changes. Skipper Brunt also started his first Barclays Premier League game of the term, with benched duo Scott Sinclair and James Morrison, who was ruled out of Scotland duty with a groin injury, plus Shane Long, who suffered a knee injury with the Republic of Ireland, making way.
After signing on deadline day, Stephane Sessegnon only returned to the club on Wednesday following international duty with Benin and he missed out due to a delay with his work permit application.
The teams sized each other up during a largely uneventful opening to the game. In the second minute, Ruiz volleyed harmlessly wide from 20 yards after McAuley had headed a right-wing centre out of the danger zone.
Five minutes later, Anichebe fashioned a shooting chance for himself inside the box after controlling Brunt’s pass and shrugging off Phillipe Senderos, but his low drive was blocked by Brede Hangeland.
Despite the lack of goalmouth activity, Albion’s near 2,000-strong following were making themselves heard behind Boaz Myhill’s goal.
And they almost had something to cheer on 19 when Brunt controlled Amalfitano’s pass and drilled a stunning left-footed effort just wide from 25 yards.
However, it was the hosts who broke the deadlock three minutes later from the first corner of the game. After McAuley and Senderos had contested Alexander Kacaniklic’s centre, the ball fell invitingly for Sidwell who smashed an unstoppable 12-yard volley past Myhill and Youssouf Mulumbu, who was marshalling the Baggies’ right-hand post.
Albion soon responded, with Amalfitano whipping a string of dangerous balls in from the right. From one such delivery in the 29th minute, Brunt towered at the far post but could only head straight at Stockdale.
Fulham thought they had added a second on 32 when Dimitar Berbatov tapped home Sidwell’s centre, but the ‘goal’ was rightly ruled out for offside.
Brunt tried to catch out Stockdale, who was well off his line, from a 40-yard free-kick on 37 and the skipper wasn’t too far away, whipping an audacious effort into the side-netting.
Albion threatened again on 44 when Billy Jones headed goalwards from another Amalfitano centre, but the right-back failed to get enough power behind his effort and Sascha Riether cleared from inside the Fulham six-yard box.
Then, in stoppage time, Mulumbu unlocked the Cottagers’ defence with an upfield ball. However, Anelka just failed to control on the edge of the box, allowing the relieved Stockdale to gather.
That proved the final incident of a half Albion will have felt aggrieved to finish a goal behind.
The Baggies started the second period positively but it was Fulham who had the ball in the net again on 52. However, Berbatov was, for the second time, rightly denied a goal by the offside flag.
Albion created a glorious chance on 54 when Brunt slipped in Anichebe. The debutant powerfully spun Hangeland but could only fire straight at Stockdale.
An identical opportunity fell to Berbatov at the other end on 58 when Ruiz threaded through the ex-Manchester United striker. This time, Myhill stood up well to produce a fine block before Jonas Olsson cleared.
Clarke range his first changes on 64, replacing Claudio Yacob and Amalfitano with Morrison and Sinclair. Moments later, Brunt tried his luck from distance but his shot rose over Stockdale’s bar.
Albion had an attacking look about them and almost got caught on the break on 66, with Berbatov sending a scissor kick just over from Ruiz’s centre.
On 71, Pajtim Kasami saw an 18-yard shot deflected wide.
Stockdale’s reflexes kept the Cottagers ahead on 74. Anichebe laid off Morrison’s lofted ball to Anelka whose first-time volley was brilliantly saved by the Fulham No.13.
Another Baggies chance went begging on 77 when Anelka lost his footing after being put clean through by Anichebe.
As the Albion pressure mounted, Clarke made his final change on 78, replacing Anichebe with Saido Berahino.
With the Baggies piling men forward, they got caught short at the back on 83 and Ruiz was mightily unlucky to see his 15-yard shot bounce down off the underside of the bar and back into play.
But McAuley earned Albion the point they had deserved when he planted an unstoppable header into the bottom left-hand corner from Brunt’s corner in the 92nd minute.
FULHAM (4-2-3-1): Stockdale; Riether, Senderos, Hangeland, Richardson (Amorebieta 67); Sidwell, Parker; Ruiz (Duff 90+1), Kasami, Kacaniklic; Berbatov (Rodallega 77). Subs not used: Etheridge (gk), Zverotic, Karagounis, Taarabt.
ALBION (4-4-2): Myhill; Jones, McAuley, Olsson, Ridgewell; Amalfitano (Sinclair 64), Mulumbu, Yacob (Morrison 64), Brunt; Anelka, Anichebe (Berahino 78). Subs not used: L Daniels (gk), Dawson, Popov, Rosenberg.
GOALS: FULHAM – Sidwell (22). ALBION – McAuley (90+2).
BOOKINGS: ALBION – Jones (foul 70).
REFEREE: Lee Probert (Wiltshere).
ALBION STARMAN: Chris Brunt.