Ruben Rochina opened the scoring for Blackburn in the 32nd minute with a brilliant finish when he received the ball from Junior Hoilett on the edge of the area and without a back-lift, struck it brilliantly off the underside of the crossbar giving Mark Schwarzer no chance to see his first Premier League goal go in with style.
That goal brightened up an otherwise dour start and it motivated Fulham who replied six minutes later through Bobby Zamora who produced a fantastic finish after Danny Murphy played a ball out to the right.
Zamora managed to get around Gael Givet before opening up his body to shoot with his trusty left from the right side of the penalty area and finding some help from the far post with a pinpoint shot on goal.
Neither side had clearcut scoring chances until later in the match when Cottagers skipper Murphy completely turned Scott Dann after being played in by Clint Dempsey but was denied by Paul Robinson in the 73rd minute.
Fulham completely dominated the second half in terms of possession but were unable to pierce the Rovers defence with Dempsey's curling attempt from the top of the 'D' being kept out by Robinson just as regular time ticked over.
Blackburn's forward forays were almost non-existent in the final 30 minutes as the Cottagers got right on top but the visitors held on desperately in defence to hold out for a share of the points as a wasteful Fulham outfit would be left to rue their profligacy.
Blackburn's Hoilett paid the price for a very brave act when he collided with an advancing Schwarzer as both players contested an aerial ball just outside the area which forced a long break in injury time with the Australian keeper receiving a caution for his efforts. Early reports after the match suggest the Canadian international just had some concussion which is a relief after he was stretchered off the pitch in a neck brace.
The draw kept Martin Jol's Fulham in 18th position with two points in the bag whilst Steve Kean's Rovers opened their points account but sit at the foot of the league table.
TRIBAL ASKS: Is Steve Kean's job in danger at this early stage of the campaign?
Both clubs remain without a win from four games this season.