Wolfsburg's third consecutive win lifted the 2009 champions to eighth on 37 points. Sixth place at the end of the season will be enough to qualify for the Europa League.
Hamburg, the only club never to have played in the second division since the introduction of the Bundesliga in 1963, remained stuck in 14th position on 27, two points above the relegation play-off zone after their fifth defeat in six games.
After a lacklustre first half, Wolfsburg grabbed the lead straight after the restart when Iran international Ashkan Dejagah raced down the right and crossed for Mario Mandzukic at the far post to head in his 10th league goal of the season.
Hamburg equalised a minute later as Marcus Berg chipped the ball over on-rushing keeper Diego Benaglio.
Former Germany international Marcel Schaefer restored Wolfsburg's lead in the 75th minute, curling a free-kick under goalkeeper Jaroslav Drobny's body.
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