Andreasen put Mirko Slomka's men in front in the 17th minute, but they had to wait until six minutes from time before being able to celebrate as Huszti sealed the win against the nine-man Wolves on the opening weekend of the season.
Maxilimilian Arnold and Timm Klose both received their marching orders for Dieter Hecking's side, who will need to show more discipline if they are to challenge for a place in Europe next season.
While they had 11 men on the field, Wolfsburg did not look in any way inferior.
In fact, had Rob Robert Zieler not been at his best to deny Ja-Cheol Koo in the second minute, it may well have been a different story.
Andreasen then put the Reds in front when he picked up the ball in midfield before letting Mame Diouf take over and lead the ball deep into Wolfsburg territory.
The Senegalese forward did not lose sight of the accompanying Andreasen, though, and pulled the ball back to the defender, who slotted his shot through Diego Benaglio's legs to give the Reds the lead.
The Wolves roared back with Arnold biting a little too aggressively as he earned a straight red card for a foul on Karim Haggui in the 32nd minute.
Koo hit the underside of the crossbar as Wolfsburg continued to pose a threat even with a man less, but when Klose was shown a second yellow card for a block on Diouf, the chances of a recovery reduced substantially.
It took Hannover over half an hour to make their two-man advantage count, however, before Huszti relieved the growing tension inside the Niedersachstenstadion with the second shot placed through Benaglio's legs to seal victory.