Thorsten Fink's men proved to be no match for the in-form German champions, who never looked like dropping points in what was a fairly one-sided encounter
Kevin Grosskreutz and Robert Lewandowski were on target in the first half for Jurgen Klopp's men, and Kuba added a brace after the break. Lewandowski completed his double shortly after, and Jose Paolo Guerrero netted a consolation goal for HSV, who simply could not contain BVB on the day.
Hamburg struggled from the start of the game and nearly fell behind in the 12th minute when Gojko Kacar gave the ball away in the centre of the pitch, allowing Dortmund to mount a counterattack. A brilliant intervention by Heiko Westermann, however, prevented a goal as the Germany international dispossessed Lewandowski in the penalty area.
Moments later BVB were not so forgiving as Grosskreutz netted the opener. The former Ahlen man was picked out near the penalty spot by Shinji Kagawa, and put a simple finish past Jaroslav Drobny to make it 1-0.
In the following attack, however, HSV nearly drew level as an inviting cross by Dennis Aogo found Guerrero, who managed to shake off Mats Hummels before applying a header which missed the target from seven yards out.
Dortmund continued to press, however, and had the ball in the net against at the half-hour mark, but it was called off for a foul in the box. Moments later, however, BVB doubled their lead through Lewandowski after a magnificent solo run through a static home defence.
Things hardly changed after the break, as the German champions continued to press and added a third in the 58th minute. A quick break saw Lewandowski release Kuba on the right, who powered home a precise shot from outside the box into the left corner.
Things got from bad to worse for HSV 18 minutes later, when substitute Moritz Leitner was brought down in the box by Dennis Diekmeier, and Kuba converted the subsequent penalty to complete his brace.
Lewandowski also scored his second goal shortly after as he capped off a superb team move with a powerful finish to make it 5-0. Guerrero pulled one back in the 86th minute, but it was too little, too late as the damage had already been done.
The impressive win means that Dortmund, Bayern Munich and Schalke are all locked together on 37 points at the top of the Bundesliga, with Borussia Monchengladbach just a point further back.