Dieter Hecking's side clinched UEFA Champions League qualification with their win at the Imtech Arena and simultaneously increased relegation fears for the hosts, who ended with 10 men.
Josuha Guilavogui and Daniel Caligiuri were on target in either half before Johan Djourou was shown a second yellow two minutes from time.
It followed a priceless Paderborn victory over Augsburg at the Benteler Arena as Andre Breitenreiter's men picked up a first win in seven Bundesliga outings.
Elias Kachunga and Srdjan Lakic scored either side of an equaliser from Bayern Munich loanee Pierre Hojbjerg as Paderborn moved up to 16th.
Bottom side Stuttgart face Werder Bremen on Sunday with victory enough to send Hamburg bottom going into the final six games.
Third-placed Borussia Monchengladbach bounced back from their DFB-Pokal humbling at the hands of third-tier Arminia Bielefeld by seeing off Borussia Dortmund 3-1.
Oscar Wendt opened the scoring at Borussia Park after just 28 seconds, with further goals for Raffael and Havard Nordtveit enough to ensure Ilkay Gundogan's late effort proved a consolation.
Leaders Bayern Munich coped with their injury crisis to beat Eintracht Frankfurt 3-0, Robert Lewandowski at the double before Thomas Muller added a third eight minutes from time.
Pep Guardiola named just four substitutes due to a lengthy injury list, but had no problems sweeping aside Thomas Schaaf's men to maintain their 10-point lead.
Bayer Leverkusen cemented their grip on the fourth UEFA Champions League spot as they survived a late scare to beat Mainz 3-2.
Son Heung-min, Stefan Kiessling and Hakan Calhanoglu put the visitors on cruise control at the Coface Arena, although Koo Ja-cheol's two late penalties will have proven an unwanted finale for Roger Schmidt's side.
Leverkusen lead fifth-placde Schalke by 10 points, as they struggled to a goalless draw with struggling Freiburg, despite Julian Draxler's long-awaited return from a torn tendon off the bench.
