Some matches went to form, however, as second division Paderborn thumped fifth tier Rot-Weiss Ahlen 10-0, helped by a hat-trick from American striker Matthew Taylor, and Bundesliga side Nuremberg won 5-1 at third division Arminia Bielefeld.
Markus Feulner scored a 14-minute hat-trick for Nuremberg to put them in control after Tim Jerat had given Arminia an early lead.
Bundesliga pair Hamburg SV, 2-1 winners at Oldenburg, and Kaiserslautern, who won 3-0 at BFC Dynamo, also progressed and champions Borussia Dortmund sailed past third division SV Sandhausen, winning 3-0.
Japanese midfielder Shinji Kagawa, one of Dortmund's revelations last season, set up an early opener for Robert Lewandowski and fired in the second himself just before the hour. Lewandowski added the third in the last minute.
The first round is a potential minefield for Bundesliga clubs as the seeding system forces all of them to play one-leg ties away to lower division opponents.
Playing it before the league has started adds to the chances to top teams being caught unprepared and VfL Wolfsburg became the first victims when they lost at RB Leipzig on Friday.
Leverkusen, second in the Bundesliga last season, rushed to a two-goal lead in 12 minutes at Dresden through Eren Derdikyok and Sidney Sam and went further ahead after half-time with an Andre Schuerrle goal.
Dresden, promoted from the third to second division last season, hit back with headers from Sebastian Schuppen and Robert Koch in a three-minute spell.
Dresden, who were eight times winners of the old East German league but have dropped as low as the fourth tier following German reunification, levelled with another Koch goal four minutes from time.
A cool finish from defender Alexander Schnetzler three minutes from the end of extra-time sealed their win.
Bremen also took the lead at Heidenheim through Swedish striker Markus Rosenberg in the 33rd minute and missed a chance to go 2-0 ahead after the break when Markus Marin's weak penalty was saved by Frank Lehmann.
The game turned completely as Christian Sauter and Marc Schnatterer scored in a three-minute spell before the hour to give Heidenheim a 2-1 win.
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