The visitors pushed forward from the outset, coming close after just seven minutes when Andreas Lambertz's shot was well saved.
The opening goal came in the 26th minute when Oliver Fink nodded Dusseldorf ahead.
Furth almost got themselves back into the game in the second half when Tayfun Pekturk found himself with a shooting opportunity, but once again the keeper was equal to it.
The Dusseldorf defence had to be alert when Ilir Azemi rose highest to get a header in, and they successfully cleared the danger.
The visitors held out to claim all three points, moving up to seventh in the Bundesliga table.