On a bitterly cold evening in northern Germany, the Bundesliga champions had no problems against surprise package Kiel, who had knocked out two second division and one top tier team in the previous rounds.
After an early scare with goalkeeper Mitch Langerak denying the hosts at close range, Dortmund top scorer Robert Lewandowski tapped in an Ivan Perisic bicycle kick for an 11th-minute lead as Kiel conceded their first goal in the competition.
Japan international Shinji Kagawa added another, completing a swift attacking move seven minutes later and substitute Lucas Barrios grabbed his second goal in two games 10 minutes from time, volleying in a Perisic cross at the far post.
The Croat completed the rout in the 87th minute, driving a free-kick off the post and into the net.
The other quarter-finals are being played on Wednesday when Bayern Munich will be looking to book their spot in the next round against VfB Stuttgart to keep alive their own treble hopes and turn around an erratic start to the new year.
Hertha Berlin entertain Borussia Monchengladbach in the other all-Bundesliga clash while Greuther Fuerth, the only second division club left in the competition, travel to Hoffenheim.
