Robert Tesche's first-time strike gave Forest the lead before he was brought down by Emerson Hyndman and Henri Lansbury scored from the spot.
Fulham pulled a goal back when Matt Smith headed home from a corner only for Lansbury to score his second.
The Whites fall to 21st but stay up as MK Dons were relegated.
Forest climb one place to 17th after a first win in nine league games and their first away from home since 6 February.
The visitors looked the stronger side in the first half as Fulham struggled to keep possession.
They went ahead when Lansbury won a free-kick near the corner flag and sent a pass to Tesche, whose shot flew straight past keeper Marcus Bettinelli.
Forest doubled their lead from the penalty spot before Fulham hit the bar through Ross McCormack.
But the hosts did find the net as Smith's header from McCormack's delivery found the bottom right-hand corner.
Forest sealed the points when Lansbury flicked in his second from Eric Lichaj's cross.
Nottingham Forest interim manager Paul Williams:
"We've had some really good performances in recent weeks, I know results haven't shown it, but now we need to focus and to fight for the last two games.
"I am tasked with taking the side to the end of the season and that is what I am concentrating on. I want to give the fans, who were fantastic today, a good end to the season.
"The players have been fantastic, we have made little changes to players' positions. I have a philosophy and thankfully it is beginning to pay off.
"It is all credit to every single player out there today, they deserved that performance."
Fulham manager Slavisa Jokanovic:
"We don't show quality with the ball or without the ball. We make chances but generally we were very, very soft as a team.
"This is a habit for us, it is not strange giving a penalty, it is a bad habit.
"We give them so much presence, we tried in the second half to play in a different way but during the game we scored and made chances but right now we are far off how I want my team playing."
Fulham will play in the Championship again next season despite suffering a 10th home league defeat as Nottingham Forest eased to victory.