A second half strike from Jordan Rhodes was enough to give Rovers all three points in a feisty encounter at Craven Cottage.
Rovers' record signing cleverly poked home a Corry Evans volley just before the hour mark to defeat ten-man Fulham.
A cagey first half will be remembered for an awful challenge from Fulham's Shaun Hutchinson on Lee Williamson that saw the defender red carded and the Rovers man stretchered off.
But Rovers had the better of the second half with Rhodes grabbing the only goal of the game after Evans' volley deflected into the path of the striker.
Rhodes almost got a second after knocking the ball past Marcus Bettinelli only to see Dan Burn clear off the line before the Cottagers mounted a late assault on the Rovers goal.
Debutant Jason Steele saved well from Ross McCormack, whilst the impressive Shane Duffy dealt with everything that came his way to ensure a welcome three points and a first clean sheet of the season.
Rovers made three changes from the side that faced Derby on Wednesday night.
Deadline day signings Jason Steele and Shane Duffy were handed their first starts, whilst Lee Williamson returned to the starting eleven.
Making way were Paul Robinson, who missed out with a knee injury, whilst Matt Kilgallon and Craig Conway dropped to the bench.
Fulham caretaker boss Kit Symons made three changes as Marcus Bettinelli, Lasse Vigen Christensen and Bryan Ruiz att came in to start.
It was a cagey opening first half at the Cottage in which Rovers had the better of but they couldn't take their chances.
Ben Marshall, with three goals in his last two games, was the first with an attempt at goal, the midfielder racing forward but his left-footed strike lacked accuracy.
Jordan Rhodes then headed an Alex Baptiste cross over, whilst a Rudy Gestede header was claimed high by keeper Marcus Bettinelli.
Bettinelli didn't fare as well as Gestede let fly with a vicious shot on the turn, the Fulham man just about scrambling the ball away.
After Tom Cairney was caught in possession Hugo Rodallega was just wide with a superb strike before Grant Hanley glanced a Marshall corner just wide.
As the half ticked over into added time the hosts were reduced to ten men. Fulham defender Shaun Hutchinson receiving his marching orders from referee Andy D'Urso for a reckless challenge on Lee Williamson that saw the midfielder stretchered off as the half drew to a close.
Rovers were forced into a second change at the break as Tom Cairney failed to reappear at the start of the second half, his place taken by Chris Taylor in midfield.
Two minutes in and Rudy Gestede threatened from a Hanley flick but Bettinelli saved at the near post. Then an Olsson cross found Craig Conway in space on the edge of the area but he was well off target with his effort.
Just before the hour mark Rovers got the goal their play deserved. After neat approach play Conway centred from the left, and whilst Corry Evans' volley struck Dan Burn, the ball ran to Jordan Rhodes who cleverly poked home.
Rovers were then thankful for a fine Jason Steele save as a Scott Parker inspired break saw Fulham threaten. The former England man spread the ball to the left to Tim Hoogland who switched play to Ross McCormack but Steele saved his effort well with his legs.
On 69 Rovers very nearly made it 2-0 as Rhodes nudged a long ball past Bettinelli, but defender Burn was back quickly to turn the effort behind.
With nothing to lose the home side eventually pressed Rovers back as the match entered the final ten minutes.
Full back Tim Hoogland twice went close for the Cottagers, the first a first time shot that flashed just wide from a George Williams cross, the second saw him cut in from the right but his left-footed strike was well off target.
High balls were pumped into the Rovers area but they were dealt with, Shane Duffy imperious on his debut winning everything that came his way.
On the rare occasion that the Rovers back four was breached there was to be no way past Jason Steele who was also magnificent on his first appearance.
Four additional minutes were played out with any late dramas as Rovers claimed their second three-point haul on their travels this season.
FULHAM: Bettinelli; Hoogland, Hutchinson, Burn, Amorebieta; Christensen, Parker (c), Stafylidis (sub Roberts 83 mins); Ruiz (sub G. Williams 73 mins), McCormack; Rodallega.
Subs not used: Kiraly (GK), Bodurov, Kavanagh, Hyndman, Dembelé.
Booked: McCormack, Hoogland, Amorebieta.
ROVERS: Steele; Baptiste, Hanley (c), Duffy, Olsson; Cairney (sub Taylor 46 mins), Williamson (sub Conway 45+4 mins), Evans, Marshall; Rhodes (sub Varney 78 mins), Gestede.
Subs not used: Eastwood (GK), Henley, Kilgallon, King.
Goals: Rhodes 58 mins.
Booked: Evans, Taylor.