Dost struck in the 50th minute before Ivica Olic made it 2-0 three minutes later with Dost adding his second goal in the 64th minute.
Dusseldorf trimmed the deficit to 3-1 in the 71st minute with Jens Langeneke's spot kick but Diego ended all doubts with his penalty in the 78th minute which resulted in Oliver Fink being sent off.
Wolfsburg, who sacked boss Felix Magath after just five points and two goals in their first eight matches, came into the match bottom of the table but they now have eight points.
Dusseldorf remained on 10 points following their third straight defeat after no losses in their first six matches of the season.
Interim coach Gunther Kostner made six changes, including Simon Kjaer, Marcel Schaefer, Makoto Hasebe and Diego coming into the starting XI.
Wolfsburg were more attacking from the off with much more possession but neither side could create any real chances in first half until the visitors had two opportunities just before the break.
Dusseldorf defender Adam Bodzek attempted to clear a Wolfsburg corner but succeeded in sending the ball towards goal forcing goalkeeper Fabian Giefer into a scrambling save.
Seconds later in the 45th minute, Giefer pushed Dost's shot just over the bar.
Wolfsburg finally grabbed the lead five minutes after the re-start with Jan Polak sending a through ball to Olic, who crossed from the left and Dost struck just inside the near left post.
Wolfsburg doubled the advantage as Diego crossed from the right side of the box to the far left post where Olic beat Giefer and Dost scored his second goal when he tapped in Hasebe's cross.
Dusseldorf pulled a goal back when Langeneke slotted home down the left after Olic fouled Oliver Fink in the box.
But Wolfsburg made it 4-1 from the spot as Diego blasted into the lower left corner after he was fouled by Fink who was sent off.