Arjen Robben and Claudio Pizarro both scored twice as Bayern Munich claimed a 4-0 winners at home to Kaiserslautern in the second round of the DFB-Pokal.
Pizarro opened the scoring in the 11th minute and Robben made it two four minutes into the second half.
Pizarro got his second in the 58th minute and Robben completed the win for the Bundesliga leaders two minutes from time.
Bayer Leverkusen found the going rather more tough at third division Arminia Bielefeld and needed extra time before recording a 3-2 win.
Sebastian Hille put Arminia ahead after 10 minutes, but goals from Jens Hegeler (23) and Manuel Friedrich (56) put the Bundesliga side back in control.
Tom Schutz equalised in the 82nd minute to force an extra period, but Andre Schurrle got the winner four minutes into it.
Arminia had Christian Muller sent off in the 117th minute.
Fortuna Dusseldorf's all-Bundesliga tie at home to Borussia Monchengladbach also went to extra time before Nando Rafael got a 97th-minute winner.
Hannover needed penalties to see off second division Dynamo Dresden after the match ended 1-1.
Mame Diouf put Hannover ahead in the 16th minute only for Romain Bregerie to level 12 minutes later.
Extra time could not separate the sides and Hannover held their nerve to win 4-3 on spot-kicks.
Stuttgart killed off St Pauli with three first-half goals as they claimed a 3-0 home win.
Goals from Ibrahima Traore, Vedad Ibisevic and Tamas Hajnal settled the match before the break.
Wolfsburg claimed a 2-0 win at home to FSV Frankfurt thanks to second-half efforts from Diego and Bas Dost.
Elsewhere, Karlsruhe were 1-0 winners at home to Duisburg, and Kickers Offenbach saw off Union Berlin 2-0.