Gladbach spurn chance to reach summit
Former Germany international Mike Hanke put the hosts in front on the stroke of half-time by heading a free-kick from Juan Arango past Hamburg keeper Jaroslav Drobny.
The visitors should have levelled two minutes after the restart when Paolo Guerrero set up Tolgay Arslan in the box but the 21-year-old sent a thunderous drive narrowly over.
Turkey Under-21 international Arslan quickly made amends, slotting the ball in from close range in the 56th minute as Hamburg climbed to eighth on 27 points.
"We lacked punch today and offered far too little," Gladbach coach Lucien Favre told reporters after his side closed the gap on Dortmund to two points.
"We came up against a quick and strong team and did not have that in our game today."
Surprise title contenders Gladbach, who narrowly escaped relegation last season, extended their unbeaten run to seven straight games despite being without speedy winger Patrick Herrmann (broken collarbone).
Hamburg have blossomed since Thorsten Fink took over as coach in October. They have risen from last place and are now in the running for a European spot.