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.
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.
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.
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.
