Nelsen applied the lightest of touches to Benni McCarthy's 24th-minutefree-kick to put Rovers within touching distance of their first three-point haulsince November.
Defender Chris Samba had settled the home side's nerves with a fortuitous 24thminute opener after he ricocheted home an attempted clearance by former RoverDamien Duff.
Crucial: Ryan Nelsen heads home Blackburn's second
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 thebar, Fulham threatened little.
It proved a winning gamble for boss Sam Allardyce who dropped talisman DavidDunn to the bench after the rigours of Thursday's Carling Cup defeat to AstonVilla.
There was little doubt the strain had been showing on the Rovers boss aftertheir long winless streak which saw them slide back within reach of therelegation zone.
And there were lingering fears over the effect of Dunn's absence during thelow-key opening stages in which the pressure on the home side to produce aresult was evident.
Rovers had a penalty claim waved away in the 14th minute when Nikola Kalinicfell under pressure from Brede Hangeland as he tried to meet Steven Reid'scross.
Get in: Chris Samba celebrates his opener
Counter-attacking brightly, the visitors created another chance in the 17thminute when the dangerous Dempsey headed Stephen Kelly's cross into PaulRobinson's arms.
As the tempo increased Reid's flick-on sent Kalinic scampering into the Fulhambox 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 downa punt forward from Samba before firing a right-foot shot which Schwarzer didwell to punch over the bar.
But Rovers went ahead from the resulting set-piece with McCarthy flinging theball in and Damien Duff's boot off the line striking Samba and ricocheting backinto the net.
Tussle: Brett Emerton and Paul Konchesky battle it out
Hangeland's through-ball gave Fulham a chance to equalise on the half-hour butJohnson, 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-kickin from the left and Dempsey reacted with his acrobatic over-head kick whichstruck the bar.
Home nerves frayed as Duff shot on target then Dempsey should have done betterwhen 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 ofMcCarthy's free-kick to finally all but end Rovers' long search for a leaguewin.
Battle: Blackburn's Martin Olsson tangles with Stephen Kelly
Fulham pressed in ragged fashion, with Robinson holding a shot from Zoltan Gerathen 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 along-range free-kick just over, then turned provider again to set up Kalinic whostumbled on the edge of the box.
Blackburn boss Sam Allardyce hints at move for Middlesbrough's Gary O'Neil JANUARY TRANSFER WINDOW 2010: All moves at every Premier League club FULHAM FC