Hamburg dropped below VfB Stuttgart into 17th place on goal difference after slumping to their sixth consecutive away defeat despite taking the lead.
Both teams have 24 points, two below Nuremberg, and six games each to play.
Stuttgart are in the relegation play-off spot.
The match started promisingly for three-times Bundesliga winners and former European champions Hamburg when Cameroon forward Jacques Zoua headed in Hakan Calhanoglu's cross just before the half hour.
Hamburg were close to a second when Rafael van der Vaart headed just wide in what proved a costly miss.
Three minutes later, Gladbach were awarded a penalty for a handball by Michael Mancienne and, although Filip Daems saw his weak effort saved by Rene Adler, the Belgian defender followed up to score from the rebound.
Calhanoglu was twice close to putting Hamburg back in front in the second half, before two quick goals from sixth-placed Gladbach finished the visitors off.
Rafael put the finishing touch to a neat move in the 75th minute and Alvaro Dominguez took advantage of poor marking to add the third three minutes later.
"The first half was good from us, but you need a bit of luck in our position, and we played against a class team," Van der Vaart told Sky. "We dominated the game at times and we had our chances."
Later in the day Werder Bremen came from behind to win 2-1 at Hannover in dramatic fashion and leapfrog them into 12th place.
Franco di Santo and Sebastian Proedl netted in the second half - the latter in stoppage time - after Szabolcz Huszti broke the deadlock for the hosts two minutes prior to half-time.
- Sports & Recreation
- Rafael van der Vaart
- VfB Stuttgart