Hamburg embarrassed by 10-man minnows in DFB Pokal
Hamburg's misery was compounded by the fact that Osnabrueck played most of the game with 10 men, after defender Marcel Appiah was sent off on 19 minutes.
After taking the lead through a smash-and-grab goal from Halil Savran five minutes before half-time, the underdogs struck again through Marc Heider on the counter-attack with an hour played.
Disastrous defending from Hamburg then allowed Ahmet Arslan to add a third in the 71st minute
Though Bobby Wood pulled a goal back from the penalty spot, it was too little too late for Hamburg.
'We have to be very self-critical, Hamburg sporting director Jens Todt told Sky.
'We had one man more than them for 70 minutes and we still couldn't win; we defended badly.
RB Leipzig had an easier afternoon, reaching the second round with a 5-0 win against sixth-tier Dorfmerkingen.
Goals at the beginning of each half from Marcel Sabitzer gave Leipzig a 2-0 lead, before Timo Werner, Yussuf Poulsen and Naby Keita added three more in quick succession.
Hanover survived an early scare to beat fourth-tier SC Bonn.
The top-flight club went behind to a Lars Lokotsch goal on 20 minutes, but goals from Niclas Fuellkrug, Kenan Karaman, Sebastian Maier and Martin Harnik saw them take a 6-2 victory.
Fourth-tier Schweinfurt provided a further upset, knocking out second division SV Sandhausen with a 2-1 victory.
Elsewhere, Greuther Fuerth and Bochm beat lower league opposition, while Union Berlin secured a 2-1 victory over Saarbruecken in extra-time.
A late penalty saw FC Ingolstadt beat local rivals 1860 Munich, and Wolfsburg laboured to 1-0 win against Norderstedt.