Hamburg, who have taken only one point in the last three league games and won two of their last 10 matches, are in sixth place on 44 points, four behind Werder Bremen in fifth.
The fourth and fifth-place finishers will compete in next season's Europa League competition. Gladbach grabbed the winner two minutes from half time when defender Roel Brouwers tapped in from close range.
Hamburg brought on Burkina Faso midfielder Jonathan Pitroipa and Peru striker Paolo Guerrero, in his first match back since tearing his cruciate ligaments in September, in the second half but failed to seriously threaten the hard-working hosts.
Gladbach moved up to 34 points in 12th place and all but secured their place in the Bundesliga next season.
Schalke 04 on Saturday went two points clear at the top of when they defeated fellow title contenders Bayer Leverkusen 2-0 with both goals coming from top scorer Kevin Kuranyi.
Bayern Munich dropped to second on 56 points after slumping to their second straight league defeat, this time against visiting VfB Stuttgart 2-1 on Saturday. Leverkusen are third on 53 points.
NEWS:Schalke take top spot in Germany
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