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Sebastien Haller's first-half penalty clinched Eintracht Frankfurt a 1-0 win and condemned the Bundesliga's bottom club Cologne to a fifth straight defeat.
Haller struck the only goal from the penalty spot midway through the first period and that was enough to seal Frankfurt's second league win of the season.
Cologne had their chances, but visiting goalkeeper Lukas Hradecky was in fine form and the home side slipped to a sixth straight defeat in all competitions.
Haller converted the decisive spot kick in the 22nd minute after Cologne goalkeeper Timo Horn had brought down Mijat Gacinovic in the penalty area.
Cologne's Japan international Yuya Osako fired narrowly over the crossbar and saw another second-half effort superbly saved by Hradecky, who also kept out Leonardo Bittencourt's 70th-minute header.
Frankfurt midfielder Gacinovic was denied his side's second by Horn's fine low save, while Cologne striker Jhon Cordoba's effort from a tight angle was kept out by Hradecky.