Steve Kean's struggling side had taken the lead through a fine strike from Ruben Rochina in the first half, but Zamora equalised soon after to leave Blackburn still waiting for their first league win this season.
There was more bad news for Kean as midfielder David Hoilett was stretchered off in stoppage time wearing a neck brace after a nasty collision with Fulham goalkeeper Mark Schwarzer.
Fulham are also without a victory in their first four league games and, like Blackburn, they were unable to climb out of the bottom three after a scrappy encounter in west London.
"He's got three or four stitches in the side of his head and a bang on his eye," Kean said of Hoilett's injury.
"It's not a great challenge and he'll have some concussion. It's a bad one.
"He was out for a little bit of time and it might affect him for the next game, but he'll be fine."
Cottagers boss Martin Jol gave Costa Rica striker Bryan Ruiz his debut following a ?£10.6 million switch from FC Twente on transfer deadline day, while fellow new boy Zdenek Grygera, the former Juventus defender, was on the bench.
Kean handed a debut to former Birmingham centre-back Scott Dann, who joined Rovers just before the transfer window closed, but it was Blackburn's more creative players who caught the eye early on.
Rovers were quickly into their stride and Rochina twisted and turned on the edge of the box before forcing Schwarzer to save.
David Goodwillie was next to threaten as he went close with an audacious overhead kick that flew just over the crossbar.
Fulham were forced to make an early change when defender Aaron Hughes picked up a knock and was replaced by Stephen Kelly in the 20th minute.
Blackburn midfielder Steven N'Zonzi drove a long-range effort narrowly wide as the visitors kept up the pressure and their dominance was rewarded in the 32nd minute.
Former Barcelona trainee Rochina took possession from Hoilett on the edge of the area and unleashed a superb drive that went in off the underside of the bar.
Fulham could have few complaints about that but they equalised just six minutes later when Zamora timed his run perfectly to beat the offside trap and steer a shot past Paul Robinson from a tight angle.
Jol opted to send on Mousa Dembele in place of Ruiz after an ineffective debut, but there was a definite drop in quality from both sides after the break, with few chances on offer as passes went astray far too often.
The only opportunities fell to Fulham, but Robinson was equal to strikes from Danny Murphy and Clint Dempsey before Hoilett's injury agony marred the clash.
Source: AFP
Source: AFP