The four teams join Hamburg, Schalke 04, second-division Mainz and reigning cup-holders Bayern Munich in the last eight, which will feature six of the current top 10 from the country's top division.
First-half goals from Patrick Helmes, Michal Kadlec and Renato Augusto secured Leverkusen a 3-1 win at home to Energie Cottbus, while second-half strikes by Hugo Almeida and Claudio Pizarro gave Werder Bremen a 2-1 comeback victory at Borussia Dortmund.
A second-half effort from forward Ronny Konig earned second-tier Wehen an unexpected 1-0 win over Bundesliga strugglers Karlsruhe, while Wolfsburg crushed Hansa Rostock 5-1.
Bayern showed few signs of rustiness as they roared to a thumping 5-1 win at Stuttgart on Tuesday, in their first fixture since the German winter break began at the end of December.
A fine opener from Bastian Schweinsteiger set them on their way, with Franck Ribery, Luca Toni, Ze Roberto and another Schweinsteiger strike establishing a crushing margin of victory.
France midfielder Ribery was even able to chip a soft 21st-minute penalty straight into the arms of Stuttgart goalkeeper Jens Lehmann after Arthur Boka had been penalised for hand-ball.
Germany international Mario Gomez tapped in a late consolation for the home side.
Elsewhere on Tuesday, a hat-trick from Croatian striker Ivica Olic gave Hamburg a 3-1 win at home to second-division 1860 Munich, while Schalke 04 saw off third-tier Carl Zeiss Jena by four goals to one.