Hamburg thrashed fourth-division Meppen 7-1 away in the first round of the German Cup on Sunday, while Bochum became the first top-flight side eliminated.
Hamburg, who won the European Cup in 1983 but have been in the second division since a first-ever relegation in 2018, were 2-0 up at halftime before scoring five goals in the second period.
Bochum lost 1-0 at second-flight Regensburg, becoming the first Bundesliga side booted out of this year's Cup competition.
Top-flight Augsburg came from a goal down to beat Viktoria Berlin 4-1 away to ensure their progress to the second round.
On Saturday, Borussia Dortmund and RB Leipzig both defeated their lower-division opponents by 4-1 scorelines.
On Friday, Bayern Munich beat second-division Ulm 4-0 in Vincent Kompany's first competitive game in charge of the club.