Rovers suffered heartache at the death as a Bobby Zamora penalty settled a pulsating encounter at Craven Cottage.
Damien Duff fired the home side in front on 37 minutes before Grant Hanley levelled just before the break.
Duff regained the lead for Fulham but again Rovers hit back quickly, Junior Hoilett volleying home from close range after good pressure.
Both sides pressed for a winner, but it was handed to Fulham when referee Mark Clattenburg awarded them a penalty with a minute remaining. Bobby Zamora making no mistake from the spot.
Tempers flared at the end with Gael Givet getting a straight red for dissent, the result harsh on Rovers who would have been full value for a point.
The fallout from the 4-1 defeat at Aston Villa meant six changes from the manager for the Craven Cottage clash.
Steve Kean was able to welcome back Christopher Samba from illness and Gael Givet and Junior Hoilett from injury, whilst Steven Nzonzi, Jason Roberts and Mame Biram Diouf stepped up from the substitutes bench.
On a chilly afternoon in west London, the match was slow to get going, Rovers forcing the first effort at goal on four minutes, Steven Nzonzi nodding the ball forward to Jason Roberts who turned well and shot near post but Mark Schwarzer made the save.
It wasn't until the 16th minute that the home side threatened, former Rover Damien Duff picking out Andy Johnson at the near post, the striker flicking the ball just wide, again at the near post.
Rovers countered with Roberts heading over Salgado's centre, then Martin Olsson saw a strike from the edge of the area deflect wide with Schwarzer scrambling across his box.
The chances continued to alternate, only a brilliant stooping header from Grant Hanley stopped Johnson connecting with another near post centre from Duff, whilst following a quick break Junior Hoilett found Mame Biram Diouf, but his shot was saved by the legs of Fulham's Aussie 'keeper.
From the resulting corner Rovers would go even closer, Olsson firing the ball over for Grant Hanley to head goalwards but Aaron Hughes headed off the line.
On 31 minutes Paul Robinson saved well to stop a smart shot from Dickson Etuhu, but the Rovers number one will have been disappointed to concede the opening goal some six minutes later when after given far too much space, Damien Duff cut in from the right to shoot near post, Robinson allowing the ball to squeeze underneath him and into the net.
Rovers hit back a minute into time added on at the end of the first half and it was no less than they deserved. Martin Olsson's corner from the right was kept alive long enough for Steven Nzonzi to poke the ball towards Grant Hanley, he looked to steer the ball into the far corner, the ball deflecting off Brede Hangeland and into the opposite corner to wrong-foot Schwarzer.
As has been the case all too often this season, Rovers started the second half on the back foot. Stemming from when Chris Samba almost diverted a centre into his own net, the home side pressured Rovers for almost fifteen minutes after the restart.
Grant Hanley had been imperious at the back for Rovers, twice making important blocks to stop Fulham efforts, but there was little he could do when Fulham regained the lead on 59 minutes.
After a spell of possession on the right, Johnson and Dembele combined to find Duff and again, with too much space afforded to him, cut inside and fired though the legs of Samba, the ball creeping into the corner of the net with Robinson having no chance.
Rovers very nearly hit back immediately, when from a Hoilett corner, Mark Schwarzer got no purchase on his punch, Mame Biram Diouf sent a looping header goalward that seemed destined for the back of the net until Chris Baird headed behind from under his own cross bar.
The visitors weren't to be denied however, and it was through sheer persistance that they drew level once again.
Mame Biram Diouf through the ball into the area, Fulham couldn't clear, Givet and then Roberts kept the ball alive before it dropped invitingly to Junior Hoilett to volley home from ten yards out.
Fulham boss Mark Hughes responded by throwing on Bobby Zamora and the England striker went close with his very first touch. A free-kick on the right of the area saw Zamora step up and send the ball forwards that deflected off Diouf and needed Robinson to be alert to push it aside.
Morten Gamst Pedersen replaced Gael Givet then Ruben Rochina replaced the tiring Junior Hoilett. Between the two substitutions Mame Biram Diouf broke quickly into the area, he squared it for Junior Hoilett who tapped it into the path of Jermaine Jones but he placed his shot wide of goal.
Hat trick hunting Damien Duff saw a shot deflect wide off Samba, whilst Jason Roberts shot tamely at Schwarzer, then Paul Robinson made a brilliant save to deny Johnson from close range as both sides sought the winner.
But with 90 seconds of the 90 remaining Fulham were handed all three points with a very tame penalty decision.
A corner into the Rovers box was cleared only for referee Mark Clattenburg to blow his whistle and point to the spot. The man in black seeing an infringement that few in the 25,000 crowd will have done. Grant Hanley deemed to have held back Aaron Hughes.
Bobby Zamora took up the penalty duties, making no mistake with a low shot down the middle with Robinson diving to the side.
At the full time whistle Gael Givet let his emotions get the better of him by sprinting on the pitch to confront the referee, resulting in a straight red card for the Frenchman.
It was a bitter blow to suffer for Rovers, they had given as good as the opposition and more than deserved a point for their endeavours.
FULHAM: Schwarzer, Salcido, Hangeland, Baird, Johnson, Murphy (c) (sub Zamora 70 mins), Duff, Hughes, Etuhu, Dempsey, Dembele (sub Kakuta 78 mins).
Subs not used: Stockdale, Kelly, Gudjohnsen, Greening, Davies.
ROVERS: Robinson, Salgado (sub Emerton 90 mins), Samba (c), Hanley, Givet (sub Pedersen 77 mins), Hoilett (sub Rochina 82 mins), J. Jones, Nzonzi, Olsson, Roberts, MB Diouf.
Subs not used: Bunn, Kalinic, Andrews, Santa Cruz.
Booked: Etuhu, Baird (Fulham), Roberts, Hanley, Jones (Rovers).
Off: Givet (Rovers).