The home side were reduced to 10 men as Bobby Wood received a second yellow card for a foul after 71 minutes, but - despite Hamburg's efforts to hold on for maximum points - Wolfsburg's 4-1 triumph over bottom side Cologne meant they could not be caught.
Hamburg have battled bravely against the drop in recent seasons - finishing 16th in both the 2013/14 and 2014/15 seasons only to survive by winning relegation play-offs against Greuther Fürth and Karlsruhe respectively - but a chronic lack of goalscoring talent saw them finally perish on Saturday afternoon despite a 2-1 win at home to Borussia Monchengladbach.
All good things must come to an end.
The clock had previously recorded the amount of time the club had been in the Bundesliga.
Hamburg had taken an early lead through Aaron Hunt before Gladbach's Josip Drmic levelled the score just before halftime.
Until today, Hamburg were the only club never to face relegation from Germany's top flight competition since its formation in 1963.
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At the other end of the table, Hoffenheim pipped Bayer Leverkusen and RB Leipzig to fourth place, as they beat Borussia Dortmund 3-1 to secure Champions League Football next season.
When news that the full-time whistle had blown in Wolfsburg filtered through, Hamburg fans invaded the pitch at the Volksparkstadion, igniting flares and forcing a lengthy suspension as order was restored.
Dortmund goalkeeper Roman Buerki gifted Hoffenheim possession with a awful clearance on 26 minutes, allowing Andrej Kramaric to fire the home side in front.
A brace from Jean-Kevin Augustin and goals from Timo Werner, Dayot Upamecano and Ademola Lookman helped Leipzig to a frantic 5-2 win over Hertha Berlin.
That placing will see Stuttgart join Leverkusen and Leipzig in the Europa League, providing Frankfurt do not overcome Bayern in next weekend's DFB-Pokal final.
Tassos Donis rocked Bayern again with a goal on the counter-attack before Chadrac Akolo and Ginczek struck to confirm the shock result.