A last-gasp goal from former favourite Tom Cairney broke Rovers hearts at Ewood Park.
The home side looked well on their way to claiming a first clean sheet of the campaign after a hardworking display, until the former midfielder grabbed the winner deep into added time at the end of the match.
The first half saw little in the way of goalmouth chances, Danny Graham going close for the hosts, whilst Neeskens Kebano saw a long-range strike kept out by Jason Steele.
The match opened up in the second half with Graham, Hope Akpan and Anthony Stokes all going close, but it was the visitors who snatched the points at the death when a clearance upfield fell to Cairney and he lashed home from just inside the box.
The result maintained Fulham's unbeaten start to the season, whilst Rovers still await that elusive first league win.
Rovers made seven changes changes from the side that needed extra-time to progress through to the third round of the EFL Cup on Tuesday night.
Boss Owen Coyle handed debuts to Friday signings Tommie Hoban and Derrick Williams, whilst Jason Steele, Gordon Greer, Ben Marshall, Danny Graham and Danny Guthrie all returned to the starting line-up.
Fulham, who were also victorious after 120 minutes in midweek, changed their entire team, with former Rover Tom Cairney in from the start, whilst Ryan Tunnicliffe was named amongst the substitutes.
The new-look Rovers were quickly out of the traps at Ewood Park, fashioning the first chance of the game after just eight minutes.
A lofted forward pass from Jason Lowe saw Danny Graham beat the offside trap, but having got the ball under control and cut inside, the striker put his left-footed shot just over the bar.
But despite that early opportunity for Rovers, there was little in the way of goalmouth action for either side in what was proving to be a tight first half. New boys Williams and Hoban dealing with everything that came their way in defence.
Fulham came more into the game as the half wore on, but only once did they threaten the Rovers goal.
On 35 new signing Kebano claimed a loose ball in the centre of the park, he struck well from 25-yard yards but Steele in the Rovers goal was equal to his efforts as the keeper palmed the ball behind.
The resulting corner kick saw a headed opportunity for the Congolese attacker, but it was well wide of goal.
A late free-kick from Ben Marshall gave Rovers the opportunity to lead at the break, but the midfielder's effort went straight into the wall.
Unchanged at the break, Rovers went straight onto the attack at the start of the second, half, coming close to taking the lead inside a minute of the turnaround.
A clever ball between two defenders by Marshall saw Graham race in on goal, but the striker's effort was tipped just past the far post by Fulham keeper David Button.
The visitors went straight up the other end with two chances in as many minutes. A low shot from full back Ryan Sessegnon was followed by a header from Matt Smith, but both were easily gathered by Steele.
Rovers were then given a scare when Steele failed to hold a high ball into the box when under pressure from Sone Aluko, but Williams was on hand to clear the danger.
A nasty clash of heads between Guthrie and Hoban looked like Rovers would have to make a double change just past the hour mark, but whilst on-loan defender Hoban was able to return to the field, midfielder Guthrie was helped off with nasty cut to his head to be replaced by Darragh Lenihan.
Hope Akpan saw a shot saved by Button, before Lenihan lashed a long-range effort wide of goal.
Anthony Stokes replaced Gallagher whilst Liam Feeney replaced Marshall and it was Irishman Stokes who was next to attempt to open the scoring with a near post shot. But whilst Button couldn't hold the effort, the former Brentford man was able to claim the loose ball ahead of the onrushing Craig Conway.
The Rovers fans urged their side on in six additional minutes at the end of the game, but their hearts were broken by a former Ewood favourite.
With the game stretched the ball dropped in the box to Cairney and he lashed home to leave Rovers still searching for their first win of the season.
ROVERS: Steele, Lowe, Hoban, Greer, Williams, Marshall (sub Feeney 82 mins), Guthrie (sub Lenihan 65 mins), Akpan, Conway, Gallagher (sub Stokes 73 mins), Graham.
Subs not used: Raya (GK), Byrne, Samuelsen, Wharton.
Booked: Akpan 76 mins, Lenihan 90+2 mins.
FULHAM: Button, Odoi, McDonald, Kebano (sub Christensen 90 mins), Parker (c) (sub Jozabed 78 mins), Smith (sub Woodrow 70 mins), Cairney, Madl, Aluko, Kalas, Sessegnon.
Subs not used: Bettinelli (GK), Malone, Readm, Tunnicliffe.
Goals: Cairney 90+4 mins.
Booked: Parker 68 mins.
Attendance: 10,464 (including 562 visiting supporters)