Mario Gotze scored a hat-trick as defending champions Dortmund hammered Hannover 5-1 to book their spot in the last eight.
The 20-year-old put Dortmund in front in just the third minute before Jakub Blaszczykowski added a second 15 minutes later
Gotze grabbed his personal second in the 40th minute but Mame Biram Diouf pulled one back for Hannover in the 79th.
However, Gotze completed his first hat-trick in professional football five minutes later while Robert Lewandowski added the fifth late on.
Stuttgart picked up a 2-1 win over lower league Cologne, with Christian Gentner and a Vedad Ibisevic penalty doing the damage before Christian Clemens could only score a late consolation.
Wolfsburg were forced to come from a goal down as they eventually won 2-1 over Bayer Leverkusen.
Fagner's own goal just after the half-hour mark had given Leverkusen the lead but Christian Traesch equalised and Bas Dost scored the winner in the last minute.
Bochum also progressed after beating second division rivals 1860 Munich 3-0, with two goals from Marcel Maltritz after an earlier Zlatko Dedic effort.
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