Cologne had even the golden chance to get back with a goal within but Hoffenheim custodian Oliver Baumann defused Mark Uth's hand ball penalty in the 77th minute.
The victory lift Hoffenheim to the seventh place meanwhile newly promoted Cologne slipped to the 11th position of the table.
Elsewhere, Schalke remain winless in their tenth consecutive match as Fortuna Dusseldorf came from behind to secure all three points on home soil.
Augsburg and bottom side Paderborn played out a goalless stalemate while ten-men Union Berlin eked out a 1-1 draw against Mainz.
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2020-09-15
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