A first win in regulation time for 11 days would see KalPa draw level with fourth-placed Ilves, and they set about that task midway through the first period, when Tim Soderlund fed the puck across the Kiekko-Espoo zone for Lasse Lappalainen to score, and register his 200th point for the club.
Cameron Hillis was called for tripping five minutes later, but it was the visitors who ended up profiting on the KalPa powerplay, as Janne Hamalainen stole possession and found Santeri Virtanen, whose initial effort was blocked, before he tucked away the rebound to score a shorthanded goal.
Tripping remained in fashion during the second period, as each side was guilty of it, yet neither could make use of the man advantage, before the Kuopio side what looked to be a killer second goal with just three seconds of the period to play.
Joona Saarelainen held the puck well behind the KE net, before drawing it back for Soderlund, whose one-timer had just enough on it to squeeze past goaltender Petteri Rimpinen.
Soderlund would be in the thick of the action again in the third period, but this time to KalPa's detriment - he was penalised twice, first for hooking and then for holding with only four minutes left, and it was on the latter powerplay that Kivikova drew level, through Kasper Kulonummi.
That sent the match to overtime, and 84 seconds in, Soderlund ensured he had played a huge part in all four periods, as he scored his second goal and third point of the match.
Saarelainen skated the length of the rink, holding off challenges, before laying the puck on a plate for Soderlund to fire home and win the match, 3-2.
KalPa climb above JYP into sixth, level on points with Lukko and one shy of Ilves. Kiekko-Espoo have now won three in regulation and lost three after regulation in their last six and remain in ninth place.