Taiwo Awoniyi headed the Reds in front from a corner on 11 minutes, a lead they would carry into the second half.
Lewis O'Brien ensured a nervy finish as he cut the deficit in half with 77 minutes played, but the hosts were unable to find a leveler as they continue their search for a second Premier League win.
The result moves Fulham up to sixth in the table while Forest sink to 19th, having not tasted victory since the second week of the season against West Ham United.
Story of the match
Following defeat to Bournemouth that saw his side give up a two-goal lead, Forest boss Steve Cooper dropped captain Joe Worrall and Jesse Lingard to the bench, bringing in Awoniyi and Willy Boly, who was making his club debut.
Fulham manager Marco Silva made two changes to the side that faced Tottenham Hotspur, with Issa Diop making his first start of the season in place of Antonee Robinson and Willian handed his maiden start with the Cottagers, coming in for Neeskens Kebano.
Diop then gave away a free-kick on the edge of the area late in the first half, but the hosts couldn't take advantage as the resulting set-piece could only hit the wall.
Willian then helped haul Fulham level as his corner was swung into the path of Adarabioyo, who climbed the highest to head past Henderson.
Just two minutes later, the visitors went in front. Palhinha crashed his fierce effort home and after some neat interplay by Decordova-Reid and Willian, Reed scored his first in a Cottagers shirt.
Andreas Pereira was next to test Henderson, with his free-kick stinging the palms of the Forest shot-stopper, who could only tip it out for a corner. Decordova-Reid then shot over the crossbar.
O'Brien gave the hosts a lifeline as he took advantage of a half-clearance by Fulham to make it 3-2, but the Reds were unable to find the goal that would have rescued a point.