Wolfsburg back on track with win at Hoffenheim
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 Kostner 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 25-metre 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 30-metre 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 Kostner, who has said he would like to stay on, has so far made a convincing argument for himself.
Elsewhere, Werder Bremen came from a goal down to edge promoted Fortuna Dusseldorf 2-1 in their first game without Allofs since 1999 with Kevin de Bruyne drilling in the winner eight minutes from time for his fourth goal of the season.
Bremen forward Nils Petersen had earlier powered in a second-half header to cancel out Jens Langeneke's 10th minute penalty for Fortuna.
The win saw Bremen, who had former Fortuna defender Assani Lukimya sent off for a second booking in the 77th, move up to seventh and back into contention for a Europa League spot.
Bayern Munich extended their lead at the top of the table to eight points despite being held to a 1-1 draw at Nuremberg on Saturday, while second-placed Schalke 04 remain on 23 points after losing 2-0 away to Bayer Leverkusen.
Champions Borussia Dortmund eased past Greuther Fuerth 3-1 to move up to fourth on 22 points, a point behind third-placed Eintracht Frankfurt for whom Alexander Meier struck twice in a 4-2 victory over bottom side Augsburg.