Kaiserslautern coach Dimitris Grammozis made no changes to his line-up that crushed Schalke 04 4-1 and the decision quickly paid off for the visitors.
They took a fifth-minute lead when Jan Elvedi rifled home after Hertha failed to clear a free kick floated into the box.
Richmond Tachie completed a quick move with a fine shot from the edge of the box to make it 2-0 and pile pressure on the hosts.
Hertha, who reached the last four in 2016, had a chance to cut the deficit three minutes after halftime but Haris Tabakovic could not beat keeper Julian Krahl from six metres.
Kaiserslautern scored again as Filip Kaloc pounced on a Hertha error in midfield, charging through and drilling in a low shot from outside the box to kill off the game.
Fabian Reese managed a stoppage-time consolation goal for Hertha.
Second division Fortuna Duesseldorf are through to the semi-finals. Bayer Leverkusen host VfB Stuttgart and Saarbrucken take on Borussia Monchengladbach next week in the other quarter-finals.
