Hertha, playing their first game under new coach Friedhelm Funkel who was named only 24 hours earlier, slumped to their seventh successive league defeat on a nightmare afternoon for teenage substitute goalkeeper Sascha Burchert.
Within seven minutes of replacing Timo Ochs, Burchert twice came rushing out of his area and headed the ball straight to opponents who scored.
Hertha looked as if they might emerge from their rut when Arne Friedrich headed them in front after only nine minutes. He ran 100 metres to celebrate with the hardcore Hertha fans but their joy was short-lived.
In the 24th minute, Hertha's Brazilian defender Kaka, under no real pressure, headed the ball over Ochs and into the net to level the match.
Ochs went off injured nine minutes later and was replaced by the hapless Burchert.
In the 38th minute, Burchert rushed off his line and headed the ball away but it landed straight at the feet of Hamburg's David Jarolim, who scored from 25 metres with the substitute keeper still out of position.
Two minutes later, Burchert again ran out of his area to make another clearance but this time headed the ball straight to Hamburg's Ze Roberto.
The 35-year-old former Brazil midfielder gratefully accepted the gift to score from 40 metres.
Hertha, who fired Lucien Favre last Monday, remained rooted to the bottom of the table with three points from eight games.
Leverkusen, who hammered Nuremberg 4-0 on Saturday, lead on goal difference from Hamburg. Both teams have 20 points and are unbeaten.
Werder Bremen, who have 15 points, climbed to fourth by winning 2-0 at VfB Stuttgart in Sunday's other match.
Peru striker Claudio Pizarro headed Werder in front in the third minute with his fifth league goal of the season. Aaron Hunt added the second after half-time.
