Fulham sit bottom of the table after seven matches, with their only point coming against Cardiff City last month and Magath's future is at the centre of speculation after defeat at the City Ground.
Victory for Forest sends Stuart Pearce's side back above Norwich City to the top of the table, but it required a dogged display.
Assombalonga, a club-record signing at £5.5 million, fired Forest into a two-goal lead by the 21st minute as he headed in a Henri Lansbury free-kick before converting a controversial penalty following an apparent foul on Michail Antonio.
Back came Fulham, though, and with 25 minutes to go the visitors somehow found themselves clinging on to a 3-2 lead.
Ross McCormack's 25-yard free-kick gave Fulham a lifeline in the 31st minute and Hugo Rodallega equalised from close range just after the break.
McCormack doubled his tally in the 65th minute thanks to a deflection, but Magath's men failed to shore up at the back.
Antonio equalised 13 minutes from the end before Assombalonga got his third and edged Forest ahead again a couple of minutes later.
Jamie Paterson, a second-half substitute, raced clear to wrap up the win for Forest, leaving Magath's future looking increasingly uncertain.
Derby County held off Blackburn Rovers to secure a 3-2 win at Ewood Park, extending their unbeaten run to five games in all competitions.
Although it did not start well for the visitors as Ben Marshall gave Blackburn the lead inside the first minute, Derby eventually surged 3-1 ahead.
Jamie Ward tapped in at the back post in the ninth minute to level things and Will Hughes added a second towards the end of the first half, curling a fine effort in from 20 yards.
Ward netted again in the 58th minute with a good left-footed finish following a driving run and, although Rudy Gestede poked in for Blackburn towards the end, Derby held on for all three points.
