After losing their opening three matches of the season, Hamburg promoted Zinnbauer from his role as their Under-23 coach to replace Mirko Slomka.
Hamburg had lost 3-0 to Paderborn in their opening home game of the campaign, but they produced a steely defensive performance to deny Bayern.
Pep Guardiola sent on Xabi Alonso, Mario Gotze and Robert Lewandowski in the second half and, though his side monopolised possession, infallible performances from Heiko Westermann and Johan Djourou ensured Bayern failed to score for the first time in 75 Bundesliga games.
Paderborn, considered relegation favourites in their maiden season in the German top flight, capitalised on Bayern’s slip-up to go top on goal difference – at least until Sunday.
Elias Kachunga’s tap-in – his third goal of the season – gave Andre Breitenreiter’s men a deserved 70th-minute lead, before Moritz Stoppelkamp sealed a 2-0 victory with a last-gasp goal that will decorate highlight reels for years.
The shot’s distance – 90 yards – is a Bundesliga record.
Three big misses from Adrian Ramos would, nevertheless, return to haunt Dortmund. Substitute Jairo created the opener for Shinji Okazaki, whose fourth goal in four appearances sent him outright first on the Bundesliga’s scoring chart.
It ended Dortmund’s run of six successive victories away to Mainz.
Stuttgart had the better of the play at the Mercedes-Benz Arena, but Anthony Modeste’s thumping first-half header and Tarik Elyounnoussi’s late strike earned Hoffenheim a 2-0 win.
It left Armin Veh’s team bottom, on just one point from four games.
