St Pauli were joined later in the day by fellow Bundesliga club Hanover 96 who lost 5-4 on penalties to regional league club Elversberg after a 0-0 draw at the end of extra time.
A small group of disappointed Hanover fans caused trouble outside the stadium before police moved in to break them up.
All other Bundesliga clubs avoided any unpleasant surprises in the tricky one-legged ties to advance into the second round.
Chemnitzer, who play in the northern regional league, grabbed a fifth minute lead through Andreas Richter and managed to fight off waves of attacks from the Hamburg club to clinch a memorable victory.
Last season's finalists Werder Bremen had little trouble ousting third division Rot Weiss Ahlen 4-0 in what may have been midfielder Mesut Ozil's last game for Werder, with Real Madrid negotiating to sign the gifted Germany playmaker.
Peruvian Claudio Pizarro fired them into the lead in the 28th minute before Hugo Almeida and Tim Borowski made sure of their second round spot with two goals after the interval. Marko Marin added a fourth eight minutes from time.
Ozil was taken off on the hour.
Bayer Leverkusen crushed amateurs FK Pirmasens 11-1 with Germany striker Stefan Kiessling firing them into the lead in the 36th minute. Ten more goals followed for Bayer in the second half with Patrick Helmes netting a hat-trick.
Title holders Bayern Munich are in action against fifth division Germania Windeck on Monday while Schalke 04 play third division Aalen.
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