Stuttgart arrived at the Champions League runners-up in buoyant form, unbeaten in seven league outings.
And number eight was on the cards when their Tunisian defender Karim Haggui put them in front before the quarter of an hour.
But that was to be Stuttgart's only high point as it was all one way traffic in Dortmund's favour from then on.
Greek international Sokratis Papastathopoulos started the rout, drawing the hosts back level on 19 minutes, with Marco Reus's 22nd minute contribution giving them the lead.
A second half hat-trick from Robert Lewandowski killed off the game, with Pierre-Emerick Aubameyang getting his name on the scoring charts with nine minutes remaining.
This silky win capped a superb end of October for Dortmund with Lewandowski's goal sealing victory over Arsenal in the Champions League, followed by victory over Schalke in the Ruhr derby, Klopp's contract extension until 2018 and now this Stuttgart success.
Under Klopp, they have now won 107 out of 181 league matches, just one shy of the record set by former coach Ottmar Hitzfeld, who won 108 out of 208 matches and led the club to their only Champions League success in 1997.