The match between two mid-table sides produced few goalscoring opportunities as Hannover's European ambitions take a hit.
Both teams started the game well and created chances in the opening minutes. First Ibrahima Traore's long-range effort for Stuttgart was saved and then Mame Biram Diouf's volley was blocked inside the area.
It was the away side who took control after that, though. Shinji Okazaki was causing Hannover problems in behind the midfield and should have scored midway through the half when he headed wide from close range.
Hannover had a couple of shots from distance before half time but rarely tested Sven Ulreich and the sides went in level at the break.
Okazaki was again wasteful from a good position five minutes into the second half. After finding space just inside the box, his tame shot was easily caught by the goalkeeper.
Hannover continued to push for a winner that would keep their European hopes alive, but were unable to find one and the match finished goalless.