A moment of brilliance allowed Hertha to double their lead when Marvin Plattenhardt produced a free kick to find the top corner from almost 30 yards.
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Darmstadt's hopes of getting back in the game should have been aided by Sandro Wagner just before the interval, but Rune Jarstein got a strong hand to his header to protect Hertha's two-goal advantage.
Jarstein's contribution proved to be vital as the away side pulled further ahead five minutes into the second half when John Brooks flicked a corner on to give Ibisevic the simple task of converting from close range.
A fightback never looked to be on the cards, with Konstantin Rausch's tame effort into the arms of Jarstein the closest the hosts would come to reducing the deficit.