Philip Zinckernagel's first half goal ensured Steve Cooper's side will be in this year's Championship play-offs.
The Dane capitalised on some lapse communication between Fulham centre-back Tim Ream and Marek Rodak to sneak in and poke the ball over the line.
The defeat means Fulham's confirmation as champions is delayed until at least the weekend, with the west London side needing to have bettered Bournemouth's result to be ensured of going up as the confirmed best side in the league.
Forest would have harboured hopes of perhaps a late-season push for the automatic places as news filtered in from south Wales that Bournemouth found themselves 3-0 at Swansea.