It was the first time in 37 years that the two rivals have met in Germany's top flight, but the contest was not worth the wait as they played out an uneventful stalemate.
Hosting Hannover had the better of the goalscoring chances, with their former Manchester United striker Mame Biram Diouf appearing the most likely to break the deadlock.
The Senegalese forward guided a back-post header from Szabolcs Huszti's cross wide, moments before slicing a left-footed shot high into the stands just inside the half-hour mark.
The visitors, who have the worst attacking record in the division this season, were mainly restricted to efforts from distance, none of which severely tested Hannover stopper Ron-Robert Zieler.
This result marks the first time this campaign that Braunschweig have gone two consecutive Bundesliga games without defeat, while the point moves Hannover into the top half.