A 4-4 draw in Switzerland last week had given KalPa really hope of progressing against the current champions, and those hopes only grew in the 17th minute, when Cade Borchardt struck the opening goal for the home side.
A nine-minute spell in the second period all but sealed the Kuopio side's place, as Teemu Hartikainen scored twice, either side of a Veikka Mononen goal, to put KalPa four goals to the good.
Pontus Aberg pulled one back for the Lions early in the third period, and though Dean Kukan halved the deficit with four minutes to play, it was too little, too late for Zurich, as KalPa secured a 4-2 win in the second leg to see them through to the last eight.
Following Lukko's victory over Storhamar yesterday, Ilves ensured Finland's Liiga will have three representatives in the last eight, as they won 5-2 at home to Bremerhaven to complete an 8-4 aggregate success.
The team who finished top of the Regular Season standings were pushed hard by the lowest-ranked qualifiers in the first leg, and though goals from Luke Henman and Erik Borg gave Ilves a 2-0 lead in the first period tonight, the German side hit back through Miha Verlic and Alex Friesen in the second.
However, Borg's second goal in the 40th minute settled some nerves in Tampere, before Jens Looke and Matic Torok finally put the tie beyond the "Fischtown Pinguins"' reach, wrapping up a three-goal win tonight and a four-goal victory over two legs.
Both tonight's Finnish winners will meet Swedish sides in the last eight - Ilves will take on Lulea, while KalPa will meet Brynas.