The former European champions, who have regularly struggled to avoid relegation in the past few seasons, fully deserved the three points against Hoffenheim, who missed out on a chance to move into the top four.
An own goal from Kevin Akpoguma put the hosts ahead but Hamburg had a bagful of chances to score again after the break through Bobby Wood, who hit the woodwork, 17-year-old talent Jann-Fiete Arp and Filip Kostic.
The Serbia international Kostic finally grabbed their second goal, pouncing on Hoffenheim's lack of concentration to surprise keeper Oliver Baumann with a quickly-taken free kick.
Gideon Jung made sure of the three points in the 88th minute to lift Hamburg onto 13 points on 15th place, two ahead of Freiburg, who are 16th in the relegation playoff spot.
Hoffenheim are on 20 points in seventh place, with Bayern Munich top on 29 following their 2-1 loss at Borussia Moenchengladbach on Saturday.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
