Guerrero leaves it late to seal Hamburg win
The Peruvian, perfectly set up by Mladen Petric, dinked the ball over goalkeeper Michael Rensing in the 88th minute for his sixth goal of the season.
Hamburg, who have lost only once in 12 Bundesliga outings since Thorsten Fink was appointed coach, climbed to 10th in the table with 26 points. Cologne are two behind in 12th.
The goal had been on the cards as Hamburg took control in the last 20 minutes.
Petric volleyed over the bar and almost immediately missed an excellent chance in the 73rd minute after a superb one-two with Guerrero, then Dennis Aogo had a close-range effort saved by Rensing.
Augsburg and Nuremberg produced a scrappy goalless draw in their relegation battle, livened up only by a burst of chances at both ends in the closing minutes.
The rest of the match was bogged down in midfield with neither side able to string passes together.
Augsburg are 17th in the 18-team standings and in danger of going straight back into the second division while Nuremberg are 14th with 22 points, four clear of Kaiserslautern in the relegation play-off place.