A proud run of 55 season in Germany's top flight came to an ugly end as Hamburg fans set off a flurry of fireworks, releasing a cloud of black smoke across the Volksparkstadion, forcing play to be suspended just minutes from time.
"This is an enormously painful moment for everyone at the club, which has lost one of its defining characteristics," said Hamburg president Bernd Hoffmann.
Clock ticking on Hamburg's Bundesliga future
The six-time German champions, who won the European Cup in 1983, are the only team to have played in every Bundesliga season since the league's inauguration in 1963, earning them the nickname "dinosaur".
"I am so disappointed," said Hamburg coach Christian Titz. "I was convinced that we could win the game today, and that it would be enough to stay up. The team and most of the fans gave us a worthy send-off from the top flight."
At the other end of the table, Hoffenheim pipped Bayer Leverkusen and RB Leipzig to a Champions League place next season as they beat Borussia Dortmund 3-1 to third place.
Bayern, though, were unable to give coach Jupp Heynckes an appropriate send-off in his final home game, as they stumbled to a shock 4-1 defeat to Stuttgart.
Ruthless on the break, the visitors tore through Bayern, as Daniel Ginczek, Anastasios Donis and Chadrac Akolo all found the net on the counter-attack.
"The defeat was frustrating, but we still have every reason to celebrate," said Bayern goalkeeper Sven Ulreich.
With Bundesliga lives on the line, Hamburg appeal for fans boost
Bayern celebrated with the customary on-field showers of confetti and beer, as injured players Arturo Vidal, Manuel Neuer and Jerome Boateng joined their team-mates on the pitch.
Heynckes was spared the traditional beer shower for the coach, as he disappeared down the tunnel. The 72-year-old will return to retirement after next weekend's German Cup Final against Eintracht Frankfurt.
"We wanted to send Heynckes off with a win, but we have another chance to do so next week," said defender Niklas Suele.
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