Osnabruck's Etienne Amenyido briefly cancelled out Marcel Sabitzer's early opener, before further goals from Sabitzer and Lukas Klostermann saw Leipzig wrest back control. Marcos Alvarez's 74th minute penalty then sparked fears of a late collapse for Leipzig, who were not the only top-flight side to struggle on Sunday.
2018 cup winners Eintracht Frankfurt needed a late hat-trick from Ante Rebic to beat third-tier neighbours Waldhof Mannheim 5-3. Slow out of the blocks, Frankfurt were left stunned as Valmir Sulejmani struck twice in the opening 11 minutes to put Mannheim 2-0 up.
Last season's Europa League semi-finalists quickly rallied, however, drawing level through fine goals from Daichi Kamada and Filip Kostic. Jan-Hendrik Marx's long-range screamer then put Mannheim back in front, before Rebic struck three times in the last 15 minutes to see Frankfurt through.
Both of Berlin's Bundesliga teams reached the second round, Hertha and newly promoted Union Berlin seeing off fourth-tier opposition. Union waltzed to a 6-0 victory over Germania Halberstadt, while a brace from Vedad Ibisevic helped Hertha to a 5-1 win over VfB Eichstaett.
Paderborn, also new arrivals in the top flight, were taken to extra-time by fourth-tier side Roedinghausen before eventually winning in a penalty shootout.