Sabri Lamouchi made two changes to the side that started the 1-1 draw at Derby on Saturday as Sammy Ameobi and Tiago Silva came back into the starting line-up in place of Nuno Da Costa and Ryan Yates respectively as the latter two dropped to the bench.
The visitors came inches away from grabbing the lead on 27 minutes as they counter-attacked from a Forest corner. Bobby Decordova-Reid raced through the middle third and unleashed a dipping drive that only cleared Brice Samba's crossbar by a matter of inches as it flew into the Trent End.
It was a first half of few clear-cut opportunities but Lewis Grabban did have a decent chance in the second minute of stoppage time at the end of the half. Matty Cash raced down the right-hand channel and delivered a superb ball into the box but Lewis Grabban was caught on his heels and could only divert it wide of the target.
Forest's stoppage time problems came to haunt them again, this time at the end of the first half. Arter looked as though he had lost the ball in a challenge 20 yards from goal but it rolled back to him and he lashed an outstanding effort into the top corner of Samba's net.
Lamouchi made a number of second-half changes in an attempt to get his side back into the game and on 67 minutes, two of those substitutes combined. Adama Diakhaby's ball found Alfa Semedo on the edge of the penalty area but his strike was deflected into the arms of Marek Rodak.
Some patient football from The Reds wasn't enough to break a strong Fulham side down but route-one football almost led to an equaliser with ten minutes to play. Samba's long punt down the field found its way on to the head of Da Costa but his looping effort was well gathered on the line by Rodak.
Forest probed for a leveller and had appeals for a penalty for handball waved away late on but they couldn't find a way through a resilient Fulham back line and succumbed to their first defeat since the restart.
Forest: Samba; Cash, Figueiredo, Worrall, Ribeiro; Watson (c) (Mighten 85'), Sow (Yates 46'); Ameobi (Diakhaby 57'), Silva (Semedo 64'), Lolley (Da Costa 46'); Grabban
Subs not used: Smith, Carvalho, Jenkinson, Dawson
Bookings: Ribeiro 83', Cash 89'
Fulham: Rodak; Odoi, Hector, Ream (c), Bryan; Onomah, Arter (Johansen 71'), Reed; Kebano (Knockaert 71'), Decordova-Reid (Le Marchand 87'), Cavaleiro
Subs: Bettinelli, Mawson, McDonald, Christie, Sessegnon, Jasper
Goal: Arter 45'
Bookings: Onomah 43', Odoi 90'
Referee: Robert Jones