Dortmund, who finished fifth last season, broke the deadlock in the 72nd minute after struggling to find their rhythm against a feisty Frankfurt who contained their opponents with high pressing.
England under-21 international Gittens scored with a superb strike from a tight angle that sailed into the top far corner after cutting inside the box from the right.
Frankfurt came close to a late equaliser but saw their hopes of salvaging a point dashed as Gittens scored his second after a quick counter-attack in stoppage time to earn coach Nuri Sahin his first three points at the helm.
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