Crowd trouble marred Hamburg's 2-1 home victory over Borussia Moenchengladbach, which came too late to save the club from relegation.
In Hamburg, Aaron Hunt put the home side ahead before Josip Drmic equalised for 'Gladbach.
Hamburg have played in the top flight since the league was founded in 1963, but despite defeating Borussia Monchengladbach 2-1, they were doomed when Wolfsburg beat already-relegated Cologne 4-1 elsewhere.
Jonas Hector brought Cologne level just after the half-hour mark with an exquisite chip, but Divock Origi restored the lead for Wolfsburg, edging Hamburg closer to disaster.
The famous digital clock in Hamburg's Volksparkstadion, which displays how long the club have been in the top flight, must now finally be switched off.
The end of the game was delayed as Hamburg fans set off flares causing a ten-minute delay. Titz reinvigorated the side over his eight games in charge.
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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.
There was to be no great escape for Hamburg on Saturday afternoon, with relegation to the second tier confirmed on the final day of the Bundesliga season..
Dortmund's marginally better goal difference - three goals - over Bayer Leverkusen, who conceded two goals against Hanover after leading 3-0, meant they finished fourth and grabbed the lucrative European spot which takes them into the group stage.
Everton loanee Ademola Lookman ran the show with a goal and two assists as RB Leipzig booked Europa League football by winning 6-2 at Hertha Berlin.
Elsewhere, Guido Burgstaller's bullet header saw Schalke edge Eintracht Frankfurt 1-0 and Werder Bremen left it late to triumph 2-1 at Mainz, Theodor Gebre Selassie grabbing the victor after Florian Kainz had cancelled out Jean-Philippe Gbamin's opener.