Assat came from 3-1 down at home to win 4-3 in overtime on opening night, and they were forced to respond again this time after the second powerplay they conceded resulted in Iikka Kangasniemi putting Kiekko-Espoo ahead in the 12th minute.
Kristian Nakyva grabbed an assist for the goal, but his mistake resulted in Assat's equaliser, as he was called for holding and Sakari Kostilainen found the equaliser on the powerplay with seven minutes played in the second period.
No goals in the third saw the game head to a mammoth overtime period, in which KE held on through a powerplay after a hook by Joni Jurmo, but finally, with 19 minutes played, Dylan Fabre notched Assat's second OT winner of the series, putting them 2-0 and needing one win to advance.
Also one win away from a place in the quarter-finals are Pelicans, who built on their surprise 3-1 away win on Friday night by beating JYP 3-2 at home.
The foundations for the victory were built in the first 11 minutes, as Roni Karvinen broke the deadlock before Aidan Dudas added a second within three minutes. But when Casimir Jurgens was called for cross-checking soon after, JYP took their chance and Juuso Puustinen got them back in the game.
Following a goalless second period, the visitors took less than one third-period minute to tie the game through Mikko Perttu, but unwilling to see their crucial away win from game one wiped out, the Lahti side retook the lead through Eerik Kolehmainen just three minutes later.
It's a second goal in as many playoff games for the 19-year-old who didn't find the net once in the regular season, and that was enough to put Pelicans 2-0 ahead in the best-of-five series.
After a 4-1 loss on the opening night put an end to their long winning run, IFK Helsinki found the perfect response by winning 4-1 at the home of KalPa to level the series.
Petteri Lindbohm's goal midway through the first period was cancelled out five minutes into the second by Veikka Moronen, but from the halfway mark it was all HIFK, who retook the lead through Tony Sund in the 36th minute.
Vincent Marleau then took centre stage in the final period, giving the Helsinki side a two-goal lead with eight minutes to play, and then he was on hand to stroke the puck into an empty net as the Kuopio side went for broke in the final minutes.
Hameenlinna also hit back from game one defeat against higher-seeded opponents to level their series, winning 2-0 at home to Lukko.
It took until 19 minutes into the second period when Sami Paivarinta finally broke the deadlock for HPK, and the result was wrapped up with only two seconds left in the match, when Cameron Wright found the empty net to score his first goal in six games.
Lukko will feel this was a missed opportunity, given they had 28 shots on goal to HPK's 14, but they failed to put any of them past Kim Saarinen in the home side's goal.
Game three in each wildcard round series takes place on Monday 23rd March.