Hamburg clambered into mid-table and further clear of relegation trouble, as Augsburg were held at home by fellow strugglers.
The lower reaches of the Bundesliga table took centre stage on Sunday, with two fixtures seeing potentially priceless points put on the line.
Paolo Guerrero grabbed the only goal of the game as Hamburg edged out Cologne 1-0.
Guerrero finished neatly, clipping the ball over home goalkeeper Michael Rensing with two minutes to go after latching on to Mladen Petric's pass.
Tenth-placed Hamburg remain upwardly mobile under new coach Thorsten Fink, moving above Cologne who are six points above the bottom three.
Augsburg and Nurnberg played out a goalless draw in a Bavarian derby - a result which hardly helps either side in their respective battles against the drop.
The fear of losing appeared to outweigh the ambition of winning as both sides settled for a point in a cagey encounter, despite a late flurry of chances.
Augsburg created the better opportunities, but were unable to warm up their fans with an all-important goal as the point leaves them inside the bottom two.
Nurnberg managed to pull a point further clear of Hertha Berlin, but the relegation zone lurks just four points below them.