Both sides came into the match on the back of miserable starts to the season and the share of the spoils did little to lift the spirits of either sets of fans.
Fulham edged first-half proceedings but fell behind to a moment of magic from Ruben Rochina, who launched an unstoppable 18-yard drive in the 32nd minute.
The home side equalised six minutes later through Bobby Zamora's own inspired moment, although neither managed to find an all-important winner in the second period.
New signing Bryan Ruiz was handed his Fulham debut after joining from FC Twente for £10.6million.
The visitors, meanwhile, handed a debut to former Birmingham centre-back Scott Dann as Steve Kean plumped for a 4-5-1 formation led by striker David Goodwillie.
The match started at quite a tempo although it took eight minutes for either side to eke out an opportunity, with Fulham's Steve Sidwell blazing wide inside the 18-yard box.
While the home side were enjoying slightly more of the possession in the opening exchanges, Rovers looked dangerous on the break.
Rochina twisted and turned on the edge of the box before forcing Mark Schwarzer to save, before Goodwillie came close with an audacious overhead kick that flew just over the crossbar.
The Cottagers saw Aaron Hughes forced off with a knock in the 20th minute and their frustrations increased further moments later when referee Howard Webb waved away claims that Zamora was upended by Michel Salgado in the box.
Steven N'Zonzi came close with a 35-yard drive at the other end and Blackburn took the lead with a moment of genius from Rochina in the 32nd minute.
The former Barcelona starlet was found by Junior Hoilett on the edge of the box and unleashed an exquisite left-footed drive that went in off the underside of the bar.
The home faithful were audibly irked by the goal and Fulham's indifferent performance, but only had to wait six minutes for an equaliser.
Much like Rochina's goal, Zamora scored out of the blue after ghosting in from the right flank and placing a shot past Paul Robinson from an awkward angle.
Both sides made changes at half-time, with Martin Olsson coming on for Christopher Samba due to a back injury and Mousa Dembele replacing Ruiz after an ineffective debut.
Aside from a tame Mauro Formica effort, neither side was able to produce a real opening at the start of the second period.
Fulham continued to struggle in their attempts to break down Blackburn's defence-oriented line-up, while the visitors were relying on counter-attacks.
Hoilett was a rare shining light on a miserable afternoon in west London and only a last-ditch tackle from Sidwell prevented him from getting away a shot in the 57th minute.
The Cottagers had their own chance to score seconds later but heroic defending from Gael Givet prevented Zamora tapping in John Arne Riise's cross.
The game descended into a sloppy affair as rain began to hammer down at Craven Cottage, with neither side able to dominate play.
Fulham twice came close through Clint Dempsey, who had Robinson and Gael Givet to thank for thwarting the United States international.
Blackburn had a chance of their own through lone striker Goodwillie with six minutes remaining, before Dempsey again came close.
The match ended in unsavoury fashion after Schwarzer and Hoilett clashed heads in stoppage time, with the latter forced off the field on a stretcher wearing a neck brace.