The second-tier side famously knocked out Leverkusen in last year's competition - with a 1-0 quarter-final win - before losing out in the semis to eventual winners Bayern Munich.
Kaiserslautern looked on course to potentially repeat the feat when they took their Bundesliga opponents to extra-time, before Hakan Calhanoglu and Stefan Kiessling scored to secure a 2-0 win and a place in the last eight for Leverkusen.
Fellow top-tier sides Borussia Dortmund and Hoffenheim enjoyed relatively easier passages to the quarter-finals, with Jurgen Klopp's men seeing off Dynamo Dresden.
Marco Reus' injury-enforced withdrawal before the interval cast something of a cloud over his team's win but Ciro Immobile's brace ensured Dortmund of a fourth consecutive quarter-final appearance in the Pokal.
Hoffenheim had Eugen Polanski and Kevin Volland to thank for their 2-0 win over Aalen - as they made it four games unbeaten in all competitions.
The all-Bundesliga tie between Freiburg and Cologne was an eventful one, which saw the hosts progress 2-1 at the Schwarzwald Stadion.
Anthony Ujah's 17th-minute own goal was quickly followed up by a Vladimir Darida strike for Freiburg, with the Czech midfielder then missing the chance to make it three from the spot after the hour mark.
Deyverson pulled a goal back for Cologne a minute from time, but Freiburg always seemed in control and continue to have the Pokal to distract them from their Bundesliga struggles.
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