The South Korean forward scored twice, with another from Ivo Ilicevic, as Thorsten Fink's men recorded a scintillating upset win over the reigning champions
The hosts stormed into an early lead as Son Heung-Min headed home inside of two minutes and the second half was just as explosive.
Ivan Perisic equalised seconds after half-time but HSV moved back ahead with an Ivo Ilicevic shot and a sublime solo goal from Son. Perisic immediately halved the deficit for BVB but they were unable to equalise again and thus saw their proud 31-game undefeated run in the Bundesliga come to an end.
Hamburg could not have wished for a better start as they took the lead inside the opening two minutes. Rafael van der Vaart was released down the left by a flick-on and his pinpoint cross was headed home at the near post by Son, who had found space between Mats Hummels and Marcel Schmelzer.
It forced Dortmund to wake up and, after a slow start, they soon asserted themselves on the game. Lukas Piszczek's rampaging runs provided cause for concern from HSV, yet it was not until the 30th minute that Adler was called into action again.
Moritz Leitner ventured forward from deep and curled a beautiful effort from the left towards the far post. It was at a nice height for the keeper, though, and he dived across and held the ball.
Thorsten Fink's men resorted to using counterattacking play in order to exploit the space behind the BVB full-backs and although they held the advantage into the break, parity was restored 24 seconds after the restart.
Picked out in space on the left by Robert Lewandowski, Perisic produced a marvellous chipped effort at goal which floated over Adler and dropped in at the far post.
The hosts remained unperturbed, though, and following a swift break Van der Vaart slipped a through-ball to Ilicevic. He charged into the area and lashed a ferocious shot at Roman Weidenfeller's near post that the keeper should have done more to keep out.
A mad few minutes soon followed as Son tore down the right flank before cutting inside and firing a wondrous effort past the rooted Weidenfeller to double Hamburg's advantage.
With the crowd celebrating in sheer jubilation, they were forced to quickly refocus as almost instantaneously BVB pulled one back. Piszczek beat the offside trap and teed the ball up for Perisic, who provided a simple finish.
With Marcell Jansen struggling to cope with the Piszczek, Jurgen Klopp smelled blood and brought on Jakub 'Kuba' Blaszczykowski to increase the pressure. Yet Adler remained a solid wall in the HSV goal, saving from Kuba, Perisic and Mario Gotze before Maximilian Beister cleared an effort off the line in the 71st minute.
Thirteen minutes from time, Dortmund had a fantastic chance to finally equalise as Lewandowski poked the ball to the unmarked Julian Schieber. The forward opted to shoot first time and ended up scuffing his effort straight into the hands of the keeper.
By winning, Hamburg prevented BVB from breaking their 36-game undefeated streak in the league, lifting themselves out of the relegation zone in the process.