Julian Brandt's first Bundesliga strike looked to have secured a point for the visitors, but Heiko Westermann had the final say, rifling in a worthy winner on a par with Hakan Calhanoglu's sensational opening goal.
Hamburg could scarcely have wished for a better start as Calhanoglu swept home an unstoppable low drive from all of 25 yards inside four minutes. Leverkusen immediately sought out the equaliser, but Rafael van der Vaart was on hand to prevent Simon Rolfes from sticking away Heung-Min Son's inswinging corner.
The Red Shorts' defensive issues were plain to see as Stefan Kießling brought a diving save out of Rene Adler from range, but there was no faulting Mirko Slomka's men from an attacking perspective, with Michael Mancienne and Westermann almost profiting from a pair of devilishly good set pieces.
Leverkusen created enough chances to level through Stefan Kießling and Son, but it was Hamburg who ended the half on top, with long-range efforts from Calhanoglu and van der Vaart almost catching out the hitherto untested Bernd Leno late in the half.
The Leverkusen custodian had to be at his very best to keep out Calhanoglu's next effort, before Bayer 04 were gifted the softest of equalisers when Adler somehow let 17-year-old Brandt's routine-looking strike slip through his grasp and into the net from range.
It was never going to be easy for the Hamburg No1 from thereon in, but he at least went some way to atoning for that costly error with a pair of fine saves to deny Kießling and Son as Leverkusen turned the screw.
Faced with the prospect of spending another weekend in the bottom two, Hamburg's survival instinct kicked in and it was veteran defender Westermann who delivered, crashing in Dennis Diekmeier's right-wing cross with eight minutes left on the clock. There was still time for Leverkusen's Emre Can to try and snatch a point, but Adler made the decisive block.
Line-ups and statistics
It was a painful day all round for Leverkusen, and for Kießling in particular. Find out why below on the official Bundesliga YouTube channel: