Leverkusen started the game brightly, but a lack of quality in attacking areas meant that Frankfurt were comfortable at the back for long stages of the first half.
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Meier was given the responsibility of taking the penalty, and he made no mistake in handing the visitors the advantage.
Leverkusen struggled to produce a response either side of the break as Frankfurt continued to look comfortable dealing with the home side's attacking players.
Chances were few and far between in the second half, and a wayward long-range strike from Heung-Min Son summed up the frustration for the hosts.
Leverkusen finished strongly, though, and they were rewarded with an equaliser in the 83rd minute when Bellarabi used the space on the edge of the box to pick out the bottom corner with a powerful effort.