The victory, their second under Mirko Slomka, lifts Hamburg into 14th place in the table and puts two points between themselves and the relegation zone.
After a frustrating 80 minutes without a goal for Hamburg, it was Hakan Calhanoglu who finally broke the deadlock as he netted a third goal in four games with a deflected strike that caught Raphael Schafer out.
Hamburg doubled their lead with four minutes remaining as a left-wing cross was volleyed into his own net by Nuremberg defender Mike Frantz.
The hosts were denied only their second clean sheet since late October as Josip Drmic grabbed his 12th goal of the season in the final minute, but it only served as a consolation for Nuremberg who see their opponents climb above them in the table.
Fellow strugglers Freiburg picked up their first win since late January as they beat Eintracht Frankfurt 4-1.
The hosts missed a number of chances to take the lead in the first-half, with Stefan Aigner guilty of wasting three alone, and on 36 minutes they were punished as Julian Schuster opened the scoring for the visitors.
Frankfurt failed to clear a cross from the right and when the ball was put back in, it was Schuster who reacted quickest to score an overhead kick from six yards out.
Freiburg added a second nine minutes into the second half when, after a swift counter attack, Karim Guede round Kevin Trapp and rolled the ball into an unguarded net.
Frankfurt pulled a goal back when Oliver Baumann failed to hold a Joselu shot and the striker headed the loose ball into the back of the net despite the attempts of two defenders to clear.
The hosts laid siege on Freiburg's goal but were again surprised as Felix Klaus and Guede added the final two goal to complete a comprehensive win and move Freiburg out of the bottom two.
