There were Bundesliga wins for Bayer Leverkussen and Bayern Munich, while Wolfsburg and Schalke were held to draws.
Chelsea have completed the signing of left-back Baba Rahman from Augsburg.
Bayern Munich will host Hamburg on the opening weekend when the 53rd Bundesliga season gets under way on August 14.
Augsburg booked their place in the Europa League next season by beating Borussia Monchengladbach 3-1.
Liverpool give U21s more game time than Premier League rivals but top flight lags behind Europe.
Hannover celebrated their first win of 2015 to move out of the bottom three with a 2-1 victory over Augsburg.