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.
When the ball bounced in front of him on the edge of his own box, the 27-year-old midfielder combined ferocious power and accuracy to volley it into the back of an unguarded net at the other end of the field.
The shot’s distance – 90 yards – is a Bundesliga record.
Mainz and Hoffenheim also moved level on points with at the top by upsetting Borussia Dortmund and winning at Stuttgart respectively, while Augsburg beat Werder Bremen 4-2 and Schalke recovered a two-goal deficit to draw at home to Eintracht Frankfurt.
Another upset occurred at the Coface Arena. Jurgen Klopp excelled for Mainz as a player and a coach, and he watched his Dortmund side dominate the opening hour.
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.
Jairo, the 21-year-old Spanish winger, then had a hand in Matthias Ginter putting through his own net to hand Mainz a 2-0 success.
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.
Tobias Werner starred as Augsburg beat Werder Bremen 4-2 in an entertaining spectacle, while Maxim Choupo-Moting and Julian Draxler got the goals as Schalke snatched a 2-2 draw at home to Frankfurt.
The result moved Schalke on to two points from four Bundesliga matches, but left them without a win from their first six games in all competitions for the first time in 47 years.