Allofs joined this week after 13 years at Werder Bremen and sat on the bench next to Koestner, whose team have now won three out of four league games since he took over from sacked coach and sports director Felix Magath.
Wolfsburg had been bottom of the table after only one win in their first eight games, but have rediscovered their form and team spirit since Koestner was installed as manager.
Makoto Hasebe's seventh minute header and Dutchman Bas Dost's low diagonal drive in the 24th put Wolfsburg in the driving seat.
A sizzling 30-yard free-kick from Brazilian defender Naldo wrapped up the win that lifted the visitors away from the drop zone into 13th place on 14 points.
Dost could have added another after he chased down a 35-yard Diego pass but his chip over goalkeeper Tim Wiese was cleared off the line by Matthieu Delpierre.
The loss sees Hoffenheim trade places with Wolfsburg and move perilously close to the relegation zone just one point above Fortuna Dusseldorf who are 16th.
Hoffenheim, level on 12 points with 15th-placed FC Nuremberg, managed to pull back a goal through Eren Derdiyok's header in the 88th minute.
Allofs' first order of business at Wolfsburg will be to find the right coach after Magath's unsuccessful second spell at the club, but the 60-year-old Koestner, who has said he would like to stay on, has so far made a convincing argument for himself.
- Sports & Recreation