An overtime win in game five gave Ilves two chances to knock KalPa out, but one was all they required after a decisive five-minute spell midway through the game.
Before that, they took the lead in the 13th minute when Radek Kucerik went on a one-man mission straight through the middle before burying his shot, but KalPa hit back in the final minute of period one when Konsta Kapanen laid the puck back superbly for Joona Saarelainen to finish.
Talk of a seventh game was in the air five minutes into the second period, as Teemu Hartikainen and Patrick Curry combined on the left for Andreas Okany to power KalPa into the lead, but that only served to usher in a dominant period for the Tampere side.
It took four minutes for Ilves to draw level when John Byberg's pass across was tucked away by Kasper Bjorkqvist, and when Hugo Gallet was called for hooking less than a minute later, Arttu Pelli exploited the space on the powerplay to set up Matias Mantykivi to regain the lead.
Getting back to full strength didn't help the home side, who fell two behind two minutes later when Ondrej Kos picked up the puck dumped behind the net and played it back for Matic Torok to score when given far too much space by the KalPa defence.
Ilves were all but over the line until two-and-a-half minutes left, when Teemu Engberg was dismissed for elbowing. Hartikainen scored on the powerplay to reduce the deficit to 4-3, but his goal three seconds from time was too little, too late for KalPa, whose hold of the Kanada-malja will come to an end.
The Lynx progress to the semi-finals, where they were knocked out a year ago by none other than KalPa, but must wait to discover their opponents this time around.
Last year's runners-up SaiPa have kept their season alive with two late goals to secure a key 3-1 win away at Assat that puts them back in the driving seat with game seven to be played in Lappeenranta on 13th April.
The visitors went ahead after just two minutes - Eemeli Heinila was called for hooking and that was punished on the powerplay by Santari Airola, whose shot from the blue line evaded a crowd of bodies and sticks to find the net.
Just over four minutes later, Roope Talaja continued his fine series when he was perfectly placed to lash Feetu Knihti's pass into the net from close range, but that was as good as things got for the Pori side.
In fact, neither side looked to be able to find that winning moment, and overtime was less than two minutes away when the decisive third goal finally came. On a sustained attack, Saku Salminen's incisive pass across found an unmarked Otto Kivenmaki, who put SaiPa back in front.
That forced the Aces to remove their goaltender, but all that served to do was give the away side the chance to wrap up the win, as Janne Naukkarinen found the empty net under pressure to start the SaiPa celebrations in the final minute.
