The six-time German champions have never dropped out of the Bundesliga, but missed the chance to escape the relegation play-off place as Wolfsburg climbed to fourth.
With Hannover having beaten Eintracht Frankfurt on Thursday and Freiburg seeing off Borussia Monchengladbach, the battle to avoid demotion now appears to involve just four teams.
Hamburg are a point behind fourth-bottom Stuttgart and will hope Huub Stevens' men are not able to beat Schalke on Sunday.
Kevin de Bruyne and Ivica Olic added further goals either side of the interval and Wolfsburg recorded a comfortable win despite a consolation from Ivo Ilicevic and Luis Gustavo's late dismissal for two bookable offences.
They remain on course for the final UEFA Champions League place, while Mirko Slomka's men have plenty of work to do if they are to stay in the top up.
Admir Mehmedi's brace helped Freiburg to a 4-2 win over 10-man Monchengladbach, who saw Granit Xhaka sent off with the score at 1-1.
Despite the defeat, Monchengladbach remained in the final UEFA Europa League qualifying spot due to Mainz's defeat at Borussia Dortmund.
In the battle of top against bottom, there was a predictable result, although the champions had to wait until the 75th minute for Claudio Pizarro's opener, with Mario Mandzukic adding a second four minutes from time.
