Defender Chris Samba had settled the home side's nerves with a fortuitous 25th-minute opener after he ricocheted home an attempted clearance by former Rover Damien Duff.
And despite some crisp counter-attacking and the acrobatics of Clint Dempsey, who saw a 36th-minute overhead kick beat Paul Robinson but crash back off the bar, Fulham threatened little.
It proved a winning gamble for boss Sam Allardyce who dropped talisman David Dunn to the bench after the rigours of Thursday's Carling Cup defeat to Aston Villa.
There was little doubt the strain had been showing on the Rovers boss after their long winless streak which saw them slide back within reach of the relegation zone.
And there were lingering fears over the effect of Dunn's absence during the low-key opening stages in which the pressure on the home side to produce a result was evident.
Rovers had a penalty claim waved away in the 14th minute when Nikola Kalinic fell under pressure from Brede Hangeland as he tried to meet Steven Reid's cross.
Counter-attacking brightly, the visitors created another chance in the 17th minute when the dangerous Dempsey headed Stephen Kelly's cross into Paul Robinson's arms.
As the tempo increased Reid's flick-on sent Kalinic scampering into the Fulham box only for Kelly to expertly take the ball off his toes and clear the danger.
McCarthy brought the home fans to life in the 24th minute when he chested down a punt forward from Samba before firing a right-foot shot which Schwarzer did well to punch over the bar.
But Rovers went ahead from the resulting set-piece with McCarthy flinging the ball in and Damien Duff's boot off the line striking Samba and ricocheting back into the net.
Hangeland's through-ball gave Fulham a chance to equalise on the half-hour but Johnson, who narrowly beat the offside trap, blazed over from the right flank.
Fulham came even closer in the 36th minute when Danny Murphy sent a free-kick in from the left and Dempsey reacted with his acrobatic over-head kick which struck the bar.
Home nerves frayed as Duff shot on target then Dempsey should have done better when he was sent clean through but curled his shot straight at Robinson.
Rovers went further ahead in the 54th minute when Nelsen got on the end of McCarthy's free-kick to finally all but end Rovers' long search for a league win.
Fulham pressed in ragged fashion, with Robinson holding a shot from Zoltan Gera then Samba booting clear from the six-yard box after Johnson drew out Robinson.
Searching for a goal of his own after two crisp assists, McCarthy fired a long-range free-kick just over, then turned provider again to set up Kalinic who stumbled on the edge of the box.
The result lifted Rovers up to 12th in the table, three points and three places behind Roy Hodgsons' Cottagers.
Source: Team Talk
Source: Team Talk