Chances were rare between two sides who reached the knockout stages of the Europa League this season and are both keen to return next.
While Stuttgart's chances of qualifying look slim with a nine-point gap to close on sixth-place Eintracht Frankfurt, they do still have a DFB-Pokal semi-final with Freiburg to come in 10 days' time.
Hannover, on the other hand, need to start picking up points away from home after confirming once again their strength at the Niedersachsenstadion, where they have lost only once all season.
Stuttgart repeated the destructive tactics which infuriated Borussia Dortmund a week ago, and which have also been the subject of murmurings of discontent from their own fans.
They prevented Hannover from building up any momentum, albeit without showing any initiative going forwards themselves until about half an hour in, when they started to attack a little more.
Arthur Boka was proving to be a creative outlet down the left as he got forwards regularly, but his long diagonal ball was just too far in front of Shinji Okazaki.
Early in the second half, Okazaki saw his shot saved by Ron Robert Zieler as Stuttgart started to gain more courage and throw caution to the wind.
Alexandru Maxim decided to have a go from 30 yards with the ball landing on the roof of the net in the 77th minute as the visitors appeared more likely to score than their hosts.
Didier Ya Konan led Hannover's response with a hat-trick of efforts which all missed the target, but it was Stuttgart who ended the game on the attack, albeit unable to find a winner.