In-form Leverkusen, unbeaten so far this season, were favourites and would have overtaken RB Leipzig into second spot with a home win but instead are now third on 19 points, one behind Leipzig and three off leaders Bayern Munich.
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Scoring chances for the hosts were few and far between as Hertha, eager to bounce back from a 5-2 drubbing by Borussia Dortmund last week, were disciplined at the back and only rarely ventured forward.
Leverkusen's Kerim Demirbay had their best effort with a 30-metre shot in the 32nd minute.
There was equally little from the hosts after the break with Demirbay again trying his luck from distance a few times before he floated a free kick into the box in stoppage time and Lars Bender narrowly headed wide.
Hertha are in 13th place on eighth, level with Hoffenheim, who face Mainz later on Sunday.