The visitors remain outside the top four after neither side could find a breakthrough in a dull game devoid of much goalmouth action in top flight action from Germany
Clear cut chances were extremely hard to come by, as dogged defending and tenacious midfield play came to the forefront in a largely uninspiring matchup.
There was little action to speak of in the first half, with both sides struggling to establish a foothold in the attacking third or even register a shot on target.
Hannover led the way with 60 percent of the possession in the opening 45 minutes, but were unable to conjure up anything that troubled Bernd Leno in the Leverkusen goal.
The visitors emerged from the break looking to strike quickly, and a mazy run by Andre Schurrle from the left teed up Stefan Kiessling for a shot that forced Ron-Robert Zieler into a diving, but comfortable catch.
Jan Schlaudraff fashioned a genuine opportunity in the 55th minute, when his enterprising charge down the right flank led to a great ball in for Mohammed Abdellaoue, but his diving header at the near post was snared with authority by Leno.
Hannover were the stronger side at this point, with Schlaudraff in particular appearing the most likely outlet for a breakthrough. The German forward caused Leverkusen a few problems with his direct running on the right, but the profligacy of his teammates wasted most of his good work.
Leverkusen were not out of it, however, and created a chance of their own with 15 minutes remaining. Michael Ballack held the ball up well at the edge of the area and released Kiessling, who sprinted past Emanuel Pogatetz but could only drive his finish into the arms of Zieler as his momentum forced him towards the byline.
A free-kick from Andre Schurrle flashed a few inches over the bar in injury time, as both sides seemed to lack the motivation to push on for a winner.
The result sees Leverkusen remain in sixth place with 26 points, while Hannover are four points behind in eigth place.