Pierre-Emerick Aubameyang and Robert Lewandowski grabbed a brace each with Henrikh Mkhitaryan and Marco Reus also on target for Jurgen Klopp's men.
Hamburg somehow fought their way back into the game, making it 2-2 with goals from Zhi Gin Lam and Heiko Westermann, before capitulating under the force of a Dortmund side who have now won their first five games of the season.
Mats Hummels was given Klopp's backing on the eve of the game after being left out of the Germany side twice over the past fortnight, and he almost repaid his coach's faith with a header which rattled the crossbar in 13th minute.
Aubameyang went close twice before scoring at the third to put Dortmund ahead in the 19th minute.
Hamburg goalkeeper Rene Adler will take some of the blame as he failed to keep out the Gabon international's shot from a tight angle after a trademark burst of pace created room for a shot.
Aubameyang's strike partner Mkhitaryan made it two within three minutes when he finished off a fine move, scoring from just outside the area from Lewandowski's backheel.
Dortmund were threatening to run away with it but Lam had other ideas and, seeing no pass on, he chose to curl a shot past Roman Weidenfeller from 25 yards out, stunning the Westfalenstadion and seemingly doing the same to the Dortmund players.
Less than five minutes into the second half, Hamburg levelled with former Schalke defender Westermann heading Rafael van der Vaart's free-kick past Weidenfeller.
From only two shots on goal, Hamburg found themselves on level terms, but it was a situation which, given Dortmund's domination, could not endure.
Indeed only 15 minutes passed before Aubameyang restored the home team's advantage with his second of the night, again making Adler look only average with his shot.
Lewandowski got in on the act in the 73rd minute, converting Aubameyang's cross which Reus left for him, and it was five within 60 seconds as Reus chipped in after Hamburg failed to clear their lines.
Lewandowski then gave the scoreline a more realistic look with a sixth in the 81st minute.
The Pole headed in Nuri Sahin's cross to complete Dortmund's revenge mission and take them back to the top of the Bundesliga, two points clear of Bayern Munich.