Wolfsburg began their DFB-Pokal defence on Saturday with a comprehensive 4-1 win away to third-division Stuttgart Kickers.
Max Kruse sent last year's Bundesliga runners-up on their way with a headed goal in the fourthy minute, and Bas Dost made it two just before half-time.
Manchester City target Kevin De Bruyne scored two minutes after the break, and though the hosts pulled a goal back through substitute Lhadji Badiane, former Arsenal forward Nicklas Bendtner capped the scoring four minutes to time.
Bayer Leverkusen eased to a 3-0 victory at Sportfreunde Lotte. Stefan Kiessling started the scoring after 15 minutes and Hakan Calhanoglu doubled the advantage from the penalty spot early in the second half.
Lars Bender added another penalty in the 77th minute following Tim Gorschlueter's dismissal for the hosts.
Schalke had no trouble in a 5-0 win over Duisburg, who had Branimir Bajic sent off on the half-hour mark.
Klaas Jan Huntelaar had already opened the scoring by that point, and goals from Matija Nastasic, Johannes Geis, Franco Di Santo and Leon Goretzka.
Hoffenheim became the first top-tier team to go out after losing 2-0 at 1860 Munich.
Daylon Claasen scored the opener for the 2.Bundesliga team in the 51st minute and Hoffenheim failed to find a response before Fejsal Mulic added a second for 1860 in stoppage time.
Werder Bremen had to wait until extra time to find a breakthrough but eventually defeated Wurzburger Kickers 2-0 on goals from Anthony Ujah and Fin Bartels.
Anthony Modeste took advantage of a red card to Meppen's goalkeeper to score a hat trick and guide Cologne to a 4-0 win.
Modeste opened the scoring in the very first minute, then netted his second on a penalty resulting from Benjamin Gommert's 24th-minute dismissal, before finding his third in the 79th minute. Simon Zoller scored late on to complete the rout.
Stuttgart rallied from behind to fend off Holstein Kiel 2-1.
Rafael Czichos scored for the third-tier side in the 37th minute only for Stuttgart to respond through Daniel Didavi five minutes later.
Daniel Ginczek then scored on the hour mark with what proved to be the winning goal.
Eintracht Frankfurt cruised past Bremer SV 3-0 with goals from Luc Castaignos, Stefan Aigner and Gian-Luca Waldschmidt.
Among games between lower-tier sides, Giuseppe Ricciardi scored a hat trick of penalties as fifth-tier SSV Reutlingen stunned Karlsruher 3-1.
Second-division Karlsruher had Manuel Gulde sent off after 12 minuets and Daniel Gordon joined him in the dressing room in the 51st minute. Dennis Kempe brought his side back within 2-1 before a final penalty in stoppage time secured the upset.
Union Berlin lost to fourth-division Viktoria Koln, who erased Collin Quaner's first-half opener through Mike Wunderlich's goal. Jules Reimerink found the winner in the 74th minute.
Erzgebirge Aue, who were relegated from the second tier last season, defeated Greuther Furth 1-0 thanks to Simon Skarlatidis' 68th-minute goal.
Eintracht Braunschweig saw off Hallescher FC 1-0 with Hendrick Zuck scoring the only goal.