The defeat keeps the pressure firmly on Cottagers boss Felix Magath, whose side fought back valiantly after going two goals down – both scored by Assombalonga – to take the lead thanks to a Ross McCormack brace and a Hugo Rodallega strike.
But Michail Antonio managed to draw shell-shocked Forest level and a reeling Fulham side were punished by an alert Assombalonga, with substitute Jamie Paterson completing the scoring at the death.
In a bid to arrest his side’s slump, Magath made five changes to his Fulham starting XI, with Kostas Staflydis, Shaun Hutchinson, Mark Fotheringham and Hugo Rodallega all returning, while Fernando Amorebieta was handed his first outing of the campaign.
Injuries to Chris Cohen, Andy Reid and Jack Hobbs forced Forest boss Stuart Pearce into reshuffling his pack, as Robert Tesche and Ben Osborn earned their first league starts of the season, with Danny Fox also entering the fray.
Despite a bright early start, it took just nine minutes for Fulham to get that familiar sinking feeling as Forest took the lead with their first attack of the game.
Antonio was upended by Nikolay Bodurov and, from Henri Lansbury’s whipped-in free-kick, Assombalonga rose to head powerfully past Cottagers keeper Gabor Kiraly.
Assombalonga increased Fulham’s woes from the penalty spot after 20 minutes. Antonio’s brilliant run into the visitors’ area was crudely halted by Hutchinson, who was duly booked – as was Dan Burn who manhandled referee Darren Deadman – and Assombalonga fired his kick into the bottom corner.
The Fulham manager sat motionless by the dugout as chants of “Magath out” rang out from the small pocket of Cottagers supporters situated behind Kiraly’s goal.
But just past the hour mark, Jack Hunt’s foul on Staflydis presented £11million man McCormack with a free shot on goal, and he hauled Fulham back into the match by delivering a stunning set-piece past the despairing dive of Darlow for his first league goal for the Cottagers.
Rodallega should have levelled as he latched on to a through ball, but as he rounded Darlow and shot goalwards, Lichaj rushed back to clear off the line.
Bodurov fired over when unmarked in the Forest box as Fulham came out with renewed vigour, and their early energy was rewarded when Amorebieta’s cross was smartly diverted home by Rodallega.
The Reds were falling apart and rampant Fulham amazingly grabbed the lead after 64 minutes, with McCormack firing the Londoners ahead following a three-man move between himself, Rodallega and substitute Chris David.
Darlow had to get down low to keep out a McCormack effort as the former Leeds star began to rip the Forest defence to shreds, before curling another effort just wide.
But Forest awoke from their slumber to restore parity after 77 minutes as Antonio latched on to a brilliant pass from skipper Michael Mancienne to crack home a shot into the corner.
And after looking almost dead and buried, Pearce’s side suddenly found themselves ahead two minutes later when Assombalonga’s header hit a post, but he reacted quickest to stab the ball home.
Forest then sealed victory in the 89th minute when Paterson ran through on goal to calmly dispatch the ball past Kiraly from 15 yards.