A goal ten minutes from time from the outstanding Stephen Warnock snared a point after a Danny Murphy penalty and a tap-in from Diomansy Kamara had twice given Fulham the lead.
Blackburn were hindered by the early withdrawal of Benni McCarthy, who felt the full force of Dejan Stefanovic's clattering thigh-high fifth minute challenge.
The South Africa striker was replaced by Jason Roberts after a lengthy delay which seemed to unsettle Blackburn.
From their first attack Fulham manufactured a clear opportunity when Clint Dempsey's cute pass released Kamara. The Senegal striker delayed his finish, however, and Brad Friedel was able to stop his weak effort with an outstretched leg.
Lifted by the reprieve, the visitors grew into the contest with the evergreen Tugay and dependable Aaron Mokoena bossing the midfield.
Despite exerting their control, without their first-choice strike pairing, Blackburn looked strangely toothless upfront.
Jason Roberts provided a case in point in first-half injury time when he dwelled too long, having been offered a clear shot at goal thanks to the inventiveness of David Bentley.
Blackburn were made to pay for their lack of ruthlessness within five minutes of the restart when Fulham took the lead via the penalty spot.
Kamara just beat Ryan Nelsen to Hameur Bouazza's low cross and was felled by the New Zealand defender and Murphy kept his composure to send Friedel the wrong way.
Blackburn's response was immediate and should have equalised when Morten Gamst Pedersen missed a free header from Bentley's expertly flighted free-kick.
Antti Niemi was then alert to deny Roberts moments later and Aaron Hughes cleared Brett Emerton's follow-up off the line.
The Australian didn't have to wait long to restore parity, however, when in their next attack he drew his side level with a close-range effort teed up by Warnock's cross and Roberts' flick-on.
Just as it seemed Rovers would steamroller their hosts, Fulham regained the lead. Murphy's inch-perfect pass opened Blackburn up and Simon Davies supplied the cross for Kamara to convert at the far post in the 63rd minute.
Fulham could not hang on to their advantage and were caught out when Blackburn drew level through an unlikely source.
Roberts was allowed to twist into the penalty area and his low cross was prodded home by the outstanding Warnock with ten minutes remaining to snatch a draw.