Knowing JYP, Lukko and Ilves would end the night with a game in hand over them, the pressure was on KalPa to go to the league leaders and get something, only for them to give away the first two penalties of the game and concede on both resulting powerplays.
Kasper Simontaival gave Tappara the lead in the sixth minute after Filip Westerlund was called for holding, and when Ville Ruotsalainen was punished for high sticking, Oiva Keskinen used the man advantage to double the hosts' lead.
But with a powerplay of their own, KalPa gave themselves hope in the final minute of the first period through Konsta Kapanen, who then drew the Kuopio side level with the only goal of the second 20 minutes.
The turnaround was complete with less than four minutes of regulation time to play as Lukas Kanak struck what KalPa hoped would be the winner, only for Tappara to tie things up again in the penultimate minute, courtesy of Aleksi Matinmikko.
No winner in overtime saw the sides head into a shootout, and with the scores 1-1 ahead of KalPa's third attempt, Kapanen stepped up and slotted home his third goal of the match to secure a 4-3 victory.
KalPa draw level with Lukko on 100 points, but while the Rauma side weren't in action today, they were knocked out of fourth spot by JYP, who went two points clear by cruising 3-0 past hapless Vaasan Sport thanks to a Jere Lassila hat-trick and 17 saves from Oskari Salminen.
Four points down on JYP and therefore still very much in the race are Ilves, who needed a pair of empty-netters to finally see off TPS Turku 4-1, but nonetheless secure a first three-point win in four games, as TPS fell to a fourth consecutive loss.
The gap between TPS in 13th and the top 12 has widened to four points, as Hameenlinna came from 2-0 down to win 6-3 at home to Karpat, all but ending the Oulu side's hopes of reaching the postseason, as two Cameron Wright strikes helped seal a third win on the bounce for HPK.
Hameenlinna remain in 12th, however, as IFK Helsinki made light work of a trip to third-placed KooKoo, running out 5-1 winners as Sebastian Repo bagged a brace. HIFK in 11th have put eight points between themselves and TPS, while KooKoo have now lost three in a row and sit six points ahead of Lukko.
Maxime Fortier scored two as SaiPa went 4-0 up early in the second period before eventually beating Pelicans 4-2 for a second straight win that takes them nine points clear of fifth place. It's successive defeats for the ninth-placed Lahti men, but their playoff place is not under threat for now.
Finally, Assat ended a two-game losing run with a 3-1 victory at Jukurit as their slim top-four hopes officially ended, while the Mikkeli side must win their last three, hope Hameenlinna lose their last four and hope TPS pick up no more than one win to reach the playoffs.
Follow the final matches of the Liiga regular season on Flashscore.