Leverkusen were on top in the opening exchanges and came close when Andres Guardado struck a left-footed effort not too far over the top after a corner was partially cleared to him.
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There were very few chances in a scrappy game, with most efforts coming from distance. Gonzalo Castro was next to try his luck, but he could not find the target with his effort.
The closest Braunschweig came to opening the scoring in the first half was through Jan Hochscheidt, who put a shot from around 25 yards not too far wide of the post.
Just a minute into the second half, however, and the away side took a shock lead. Ken Reichel struck a shot from the angle on the left high into the net for what looked a crucial goal.
Neither side could carve out a good enough chance to take the points and Braunschweig held on for what could be a big point in their relegation battle.