Kevin de Bruyne drilled 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.
Allofs joined Wolfsburg this week after 13 years at Werder Bremen.
