The Poland striker found the net but also received his marching orders in an enthralling encounter, won by the visitors thanks to two goals from Rudnevs
Robert Lewandowski had raised hopes with an early opener, but later saw red as Artjom Rudnevs' double and two further strikes from Heung-Min Son meant BVB left empty-handed.
Dortmund went into Saturday's encounter in a rich vein of form, having recorded four straight victories, but the champions were surprised by the intense opposition they found in front of them. Hamburg pressed and harried across the pitch, belying their mediocre Bundesliga position to make life very uncomfortable in the opening minutes.
The result was a hectic, action-packed first-half, with Dortmund enjoying the first clear chance. Mario Gotze did wonderfully well to chest down a cross and break through the defensive line, but the young star could not find a finish and his shot flew wide when he should at least have hit the target.
It was a minor blip, however, as minutes BVB took the lead. Hesitation from Heiko Westermann in dealing with a long ball opened the door for Robert Lewandowski, and the striker took full advantage as he slid past Rene Adler to open the scoring.
Undeterred by that setback, HSV's response was almost instant. Dennis Aogo was released down the left with a finely-weighted pass, and his low cross was met by Artjoms Rudnevs, who turned the ball into the net with a neat close-range finish.
The visitors' next goal was a thing of beauty: Heung-Min Son broke down the right-hand side and with men in the box, appeared to be weighing up a cross. The South Korean, however, had other ideas. Sven Bender was turned effortlessly as he cut back onto his left foot, and Roman Weidenfeller had no chance with an exquisite looping shot that sent the away support into raptures.
Dortmund's task to get back into the game was made even harder by the sending-off of Lewandowski, who saw red for a brutal shin-high tackle on Per Skjelbred, before clashing with Rafael Van der Vaart.
Mario Gotze then thought he had levelled the game in the dying seconds of the half when he converted Marco Reus' pass, but the goal was correctly ruled out for an offside call against Reus, with Hamburg holding on to their lead at the end of a breathtaking 45 minutes of football.
Hamburg continued their positive, aggressive approach after the break, and in the early stages appeared the team most likely to add further to the scoreline. Aogo lost Hummels after drifting in from the left, but could not make decent contact with a low cross when the goal was at his mercy. Hummels for his part had a golden chance to level after connecting with Nuri Sahin's hopeful header, but chipped agonisingly over the crossbar.
Tempers flared again as HSV were also reduced to 10-men, following Jeffrey Bruma's scything challenge on Reus, which earnt him an automatic red card.
It did not seem to trouble the away side though and seconds later a deep cross found the head of Rudnevs who slotted the ball through Weidenfeller's legs to make it 3-1.
Insult was added to injury when Jakub Blaszczykowski was robbed of possession near his own corner flag; with the resulting cross landing squarely at the feet of Son, who gleefully turned in to mark his second and Hamburg's fourth.
Defeat leaves BVB in second place after Bayer Leverkusen could only record a draw. The result, however, gives Bayern Munich the opportunity to stretch their lead at the top to 15 points when they host Schalke.