Hannover went ahead after 28 minutes through Artjoms Rudnevs, with Ivica Olic equalising at the 35 minute mark.
But Bittencourt struck in the 50th and 72nd minutes to give Hannover the victory.
Hannover, who replaced Mirko Slomka with Korkut during the winter break, had collected just one win in the last 11 matches but improved to 21 points following the win at Wolfsburg.
The home side, who had not lost in the last nine contests, remain on 30 points.
Wolfsburg started with new signing Kevin de Bruyne in their line-up and the hosts had the first chance after seven minutes but Diego's long distance shot went just wide of the right post.
Diego was close again in the 24th minute but Hannover keeper Ron-Robert Zieler made a fine save.
The visitors grabbed the lead four minutes later as Rudnevs played a give-and-go with Mame Biram Diouf and then beat Wolfsburg keeper Diego Benaglio to make it 1-0 with Hannover's first chance.
Wolfsburg nearly equalised after 33 minutes but Olic's attempt sailed just inches right.
Olic found the back of the net two minutes later as Zieler only blocked away Maximilian Arnold's shot and the Croatian international hit home the loose ball.
After Szabolcs Huszti's free-kick went just around the right post in the 49th minute for Hannover, the visitors went 2-1 ahead a minute later.
Diego's careless free-kick was snatched by Diouf and the Senegalese international fed Bittencourt, who struck past Benaglio.
Zieler kept his team ahead with a fine save from Ivan Perisic's shot in the 66th minute.
And Hannover rewarded their keeper by moving 3-1 ahead in the 73rd minute, with Huszti freeing Bittencourt down the left side and the midfielder hitting home his second goal.
Wolfsburg tried to get back into the game but Diego's free-kick went over the wall but just inches wide in the 80th minute.
And Bas Dost's header went just wide left in the 87th minute.