Anthony Modeste scored a second-half hat trick as Cologne eased past 10-man Hamburg 3-0 at the RheinEnergieStadion on Sunday.
U.S. international Bobby Wood was sent off before the hour-mark for elbowing Cologne defender Dominique Heintz in the stomach after some shoving between the two while waiting for a free kick. Referee Benjamin Brand didn't see the incident but showed Wood the red card after consulting with his linesman.
And Modeste immediately took advantage of his absence, scoring a goal in the 61st, then adding two more in the final 10 minutes to put the game comfortably out of reach for the reeling visitors.
The victory moves Cologne to fourth place -- one point behind Hoffenheim -- in the Bundesliga table after nine rounds.
Hoffenheim moved up to third place in the table thanks to a 1-0 win over Hertha Berlin which extended their unbeaten start to the season.
Niklas Sule scored the only goal of the game to earn Hoffenheim a fifth straight Bundesliga win which took them above their guests and into the top three.
Hoffenheim are now just four points behind league-leaders Bayern Munich and two ahead of Hertha, who drop out of the top three.
Press Association contributed to this report.