Dani Schahin missed an early penalty before Bellinghausen scored the only goal in the 18th minute and Furth midfielder Jozsef Varga was sent off following his second yellow card in the 38th minute.
Dusseldorf collected their second win in three matches to improve to 27 points.
Furth have enjoyed just one win in their last 20 matches to remain bottom of the Bundesliga with just 12 points.
Dusseldorf were awarded a penalty after just three minutes as Matthias Zimmermann felled Robbie Kruse in the box. Schahin stepped up to the spot but Furth goalkeeper Wolfgang Hesl held the shot down to his left.
Furth came close after quarter of an hour but Nehrig's shot was deflected by Dusseldorf keeper Fabian Giefer against the right post and he then stopped Nehrig's follow-up.
The visitors then hit the woodwork from the ensuing corner from a bicycle kick by Nikola Djurdjic.
Dusseldorf took the lead after 18 minutes as Zimmermann sent a poor backpass towards his keeper which Bellinghausen intercepted and then shot between Hesl's legs.
Furth went a man down seven minutes before the break as Varga was awarded his second yellow card and from that point in Hesl kept Furth in the game with some outstanding saves.
He tipped Schahin's blast from nine yards over the bar in the 49th minute and stopped Stefan Reisinger's shot superbly in the 64th minute.
Hesl got a foot on Reisinger's attempt from three yards out five minutes later and again found a way to put his foot in the way of Kruse's shot in the 80th minute.
The Furth keeper was the final destination for Kruse's shot in the 81st minute and against Ken Ilso two minutes later. Hesl rushed far out of his goal to clear a dangerous ball just in front of Kruse.