Second-division Holstein, who stunned holders Bayern in January in a penalty shoot-out, took command in Wednesday's quarter-final with two goals in as many first-half minutes behind closed doors in Essen.
Alexander Muehling converted a penalty on 26 minutes before former Bremen midfielder Fin Bartels put in a long header to the far post two minutes later where Janni-Luca Serra tapped the ball home.
On 90 minutes, Bartels' replacement Joshua Mees added Kiel's third goal when his shot was deflected into the Essen net.
Essen, from German football's regional leagues, had shocked Bundesliga sides Arminia Bielefeld and Bayer Leverkusen on the way to reaching the last eight.
Later, RB Leipzig host Wolfsburg in the other quarter-final with Dortmund also through to the last four after a 1-0 win at Borussia Moenchengladbach.
Tuesday's other quarter-final was postponed as second-tier club Jahn Regensburg went into quarantine after a Covid-19 outbreak before their home tie against Werder Bremen.
Standout matches today