Hamburg left it late to punish Cologne's negative tactics with a 1-0 win at the Mungersdorfer Stadion.
Jose Paolo Guerrero scored the only goal of the game in the 88th minute as Thorsten Fink's side moved up to their highest position all season, leapfrogging Cologne and Hoffenheim to move into 10th.
Cologne spent much of the game on the back foot and could therefore have no excuses about finally having their defence breached late on.
They led Hamburg by a point coming into this game, but this was not reflected in their timid approach to the game.
Cologne were extremely defensive, breaking only once with Milivoje Novakovic caught cold in their attack when he failed to control the ball, which he received for almost the first time all game after half an hour, and Jaroslav Drobny swept up.
Things had to change in the second half if the home team were to aspire to anything more than a goalless draw, and they did.
Martin Lanig thought he had put the Goats in front from a well-worked free-kick in the 62nd minute, but the linesman's flag was rightly raised.
The disallowed goal certainly lifted the crowd and it lifted the home team too, with Odhise Roshi racing down the right and sending in a dangerous cross a minute later.
As a result, the game opened up and Hamburg started to find ways through.
Mladen Petric exchanged passed with Guerrero to break into the penalty area in the 75th minute, but his volley went wide of the far post.
Three minutes later, the Croatian was adjudged to be offside when his shot was pushed onto the post by an increasingly busy Michael Rensing.
A further five minutes had elapsed when Rensing had to make a good reflex save to deny Dennis Aogo, who latched onto Guerrero's downward header.
The Cologne goalkeeper was let down by his defence in the 88th minute, though, as Guerrero beat the offside trap to reach Petric's ball through and lift the ball past Rensing from a tight angle, with Pedro Geromel unable to make a clearance on the goal-line.
