Bayern, who agreed earlier this week to part ways with coach Louis van Gaal at the end of the season after three straight defeats in all competitions, climbed to fourth on 45 points, two behind Hanover 96, who lost 4-0 to Cologne on Friday.
"I think this was also partly a reaction to last week's defeat to Hanover," Van Gaal told reporters.
"Obviously such reactions have to be accompanied by the proper result and today we got that result.
"It is also very good preparation ahead of our match against Inter Milan," said Van Gaal, whose team take a 1-0 lead into the second leg of the Champions League last 16 tie at home against the holders on Tuesday.
The Frenchman turned scorer a little later adding Bayern's fourth with a lovely chip over keeper Frank Rost and forcing Heiko Westermann to tap in an own goal following a solo effort minutes after Thomas Muller had made it 5-0 on 79 minutes.
"I am certainly not going to step down," Veh told reporters.
"Our attitude was good and that is why I am not worried at all with our first loss in the league this year," said Dortmund coach Jurgen Klopp.
Nuremberg and Kaiserslautern snatched last-gasp wins over VfL Wolfsburg and Freiburg respectively while last-placed Borussia Moenchengladbach's defender Dante gave them a valuable point with a stoppage-time goal to draw 1-1 at Werder Bremen.
