Thomas Mueller scored a hat-trick as Bayern Munich beat Schwarz-Weiss Rehden 5-0 in the DFB Pokal on Monday, while Schalke also won.
Bayern – who are the reigning champions of the tournament – won well as expected against the fourth-tier side.
Switzerland international Xherdan Shaqiri opened the scoring after 18 minutes before Mueller bagged his first in the 45th minute.
And the German claimed his hat-trick in the first 20 minutes of the second half with two more goals before Dutchman Arjen Robben put the finishing touches on the big win with a late strike.
Schalke also claimed victory, winning 2-0 at fifth-tier Nottingen after goals from Klaas-Jan Huntelaar and Leon Goretzka.
Huntelaar scored after 30 minutes but more than 12,000 fans at the Wildparkstadion in Karlsruhe still had dreams of forcing extra time until Goretzka's strike in second-half stoppage time.
Borussia Dortmund safely negotiated their way through to the second round with a 3-0 win at fourth-tier Wilhelmshaven.
They left it late though, with scores locked level after 70 minutes before Kevin Grosskreutz, Marvin Ducksch and Robert Lewandowski netted late goals.
Last season's losing finalists Stuttgart also won on the road, claiming a 2-0 success at BFC Dynamo.
The fifth-tier outfit put up a fight but ultimately a double from Bosnian forward Vedad Ibisevic sealed their progression.
There were several shocks, with Bundesliga sides Borussia Monchengladbach, Werder Bremen, Nurnberg and the newly promoted Eintracht Braunschweig dumped out of the competition at the first attempt.
Monchengladbach lost to Darmstadt 98 of the third tier on penalties, 5-4, after 120 minutes of football saw no goals scored.
Werder were bundled out in the first round for the third season in succession as extra-time goals to substitute Tim Stegerer and Marcel Ziemer gave Saarbrucken a 3-1 triumph.
Saarbrucken also play in the third tier of German football.
There was joy for second-tier sides too, as Sandhausen beat Nurnberg 4-3 on penalties after scores were level at 1-1 after 120 minutes, while Arminia Bielefeld toppled the 10-man Eintracht Braunschweig 2-1.
Some big scorelines were also on the cards, with Hoffenheim, Kaiserslautern and Bayer Leverkusen all clinical in away wins.
Despite going goalless for the first 50 minutes, Hoffenheim thrashed fifth-tier Aumund-Vegesack 9-0.
Roberto Firmino and Anthony Modeste scored doubles, as did substitutes Sven Schipplock and Kai Herdling, as Markus Gisdol's side finished full of running.
Kaiserslautern may be in the second tier but it did not stop them making a mockery of Neckarsulmer SU in a 7-0 win while last season's top scorer in the Bundesliga, Stefan Kiessling, helped himself to two goals in Leverkusen's 6-1 win at Lippstadt 08.
Other results involving Bundesliga clubs saw Augsburg win 2-0 at RB Leipzig while Freiburg, Hannover and Eintracht Frankfurt won by the same scoreline against Neustrelitz, Victoria Hamburg and Illertissen respectively.
In the pick of the other ties, Mainz 05 edged Fortuna Koln 2-1, Wolfsburg won 3-1 at Karlsruhe, Hamburg were comfortable 4-0 winners at Schott Jena and Hertha Berlin defeated VfR Neumunster 3-2 after extra time.
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