Samba opened the scoring on 25 minutes from a Benni McCarthy corner and Nelsen added the second on 54 minutes.
The closest Fulham came was a first-half effort from Clint Dempsey which came back off the bar.
Rovers gave Steven Reid his first league start for 18 months and brought McCarthy into the starting line-up in place of David Dunn as they aimed for their first Premier League win in 10 games.
Morten Gamst Pedersen, a scorer in each of their last two league matches, failed a late fitness test on a knee problem and was replaced by Martin Olsson.
Fulham, looking for their second away win of the season, made one change from their 3-2 defeat at Stoke with Clint Dempsey coming in for injured leading goalscorer Bobby Zamora.
Samba celebrated his 100th Premier League start by firing Rovers into the lead on 25 minutes.
McCarthy earned a corner with a rasping 20-yard drive which Mark Schwarzer tipped round the post and took the flag-kick himself from the left.
It bounced off Schwarzer's legs in the goalmouth and fell to Samba, who lashed into the roof of the net for his second goal of the season.
Fulham turned up the heat in the latter stages of the first half as they chased an equaliser, with an overhead kick from Dempsey coming back off the bar following a left-wing free kick from Danny Murphy and shots by ex-Rover Damien Duff and Dempsey both bringing smart saves from Paul Robinson in the Blackburn goal.
Two minutes before the break, a smart shot from 18 yards by Olsson was saved on the line by Schwarzer.
Nelsen doubled Rovers' lead eight minutes into the second half as he joined his central defensive partner on the scoresheet with his third league strike of the season.
A free-kick was awarded on the left for a foul on Olsson, McCarthy fired it into the penalty area and Nelsen stooped to head it past Schwarzer from eight yards out.
Fulham suffered a blow on 61 minutes when Dempsey limped out of the action, but Robinson was forced into action again when he parried a stinging drive from Zoltan Gera following a corner.
But Rovers continued to look good value for their advantage, with McCarthy firing a free-kick narrowly over the bar with five minutes to go and Nikola Kalinic just failing to latch on to a neat throughball from David Hoilett shortly afterwards.