Dost scored the only goal of the goal in the 23rd minute as Wolfsburg eased their relegation worries with a win that lifts them out of the bottom four.
Furth, meanwhile, continue to prop up the standings with 12 points.
Wolfsburg came close to taking the lead after 11 minutes but Diego's shot from left of goal struck the crossbar.
The visitors did not have to wait much longer to go ahead though, finding the back of the net 12 minutes later with Diego passing to Vieirinha for a cross into the box where Dost struck home from six yards out.
Furth looked to equalise almost immediately but Lasse Sobiech headed over following a free-kick.
Wolfsburg's next chance came in the 43rd minute but Diego's shot was stopped superbly by Furth keeper Wolfgang Hesl.
Furth had a good opportunity two minutes after the break but Wolfsburg keeper Diego Benaglio made a fine save to keep out Nikola Djurdjic's attempt.
The hosts struggled to create anything during the rest of the second half but did have one last chance to equalise two minutes from time.
However, Elir Azemi could not beat Benaglio when one-on-one as Furth slumped to yet another loss.