Shinjji Okazaki scored twice in Mainz's 3-1 victory away to Hertha Berlin on Saturday afternoon.
Mainz and Hannover played out a 0-0 draw at the Coface Arena on Sunday afternoon.
Paderborn were denied a dream start to life in the Bundesliga as Koo Ja-cheol netted a penalty to salvage a 2-2 for Mainz.
Mainz coach Kasper Hjulmand has been given a vote of confidence following a second cup elimination in just over a week.
Hamburg have signed Germany international Nicolai Muller after convincing Bundesliga rivals Mainz to sell.
Lyon and PSV Eindhoven were among the teams to claim wins in Thursday's Europa League third qualifying round first legs.