A return home to face Ilves looked to be the tonic for Assat following a third loss in four last time out, as they took the lead inside two minutes through Valtteri Lipiainen.
But a three-goal spell in just over 90 seconds ensured the Tampere side were level after one period - Matic Torok and Matias Mantykivi struck for the visitors, either side of a Linus Nyman goal for the Aces.
Otsu Ylitalo's goal in the second period being ruled out following a video review meant 2-2 was how it remained with 40 minutes played, and having survived two Assat powerplays in the third period, Ilves made full use with their man-advantage in the final four minutes as Simon Johansson put them ahead.
Assat were staring down the barrel at another defeat, before regular time ended just as it started, with Lipiainen scoring with less than two minutes on the clock to save the Pori side and take the match to overtime.
Neither side could find a breakthrough in the extra period, which meant a shootout was needed to settle matters. Lukas Svejkovsky did the honours for Ilves with the first penalty, but the five consecutive misses that followed meant a 1-0 shootout win for Ilves, and 4-3 in the match.
It's back-to-back wins now for 11th placed Ilves, who sit three points inside the Playoff places.
A fourth defeat in five for Assat, coupled with a seventh win in succession for Tappara means the gap at the top is five points.
Hameenlinna, who began the night a point behind Ilves in 12th, made life tough for the other Tampere side, as when Joachim Blichfeld gave Tappara a 13th-minute lead, they responded quickly through Miska Kukkonen.
But the match's difference-maker was Benjamin Rautiainen, who scored approaching the midpoint in the game to put the leaders ahead again, and with Hameenlinna forced to go for broke late on, it was he who sealed the 3-1 victory with an empty-netter with less than a minute to play.
The race for the top four places is really heating up, as the teams lying third to sixth all won, and coincidentally they all beat the teams sitting seventh to 10th. That means there is six points between second-placed Assat and sixth-placed Lukko, who gained a third-straight win, beating TPS Turku, 4-2.
KooKoo remain in third and are now two points shy of the former leaders as they strolled to a 3-0 win over Kiekko-Espoo, who failed to score for the second match running thanks to an impressive 30 saves from Eetu Randelin.
JYP put their three-match losing streak behind them with a big 6-2 victory over KalPa, while fifth-placed SaiPa have scored 21 times in their last four matches, all ending in wins, with the latest a 4-1 success away at Jukurit.
On a night of six-pointers, the bottom four all faced each other, too - IFK Helsinki climbed out of the bottom two and were replaced by Karpat, as the capital club won 1-0 away from home. Jere Karjalainen netted the only goal in the third period, as Hugo Alnefelt made 15 stops.
Pelicans heaped more misery on bottom-of-the-table Vaasan Sport, as Patrik Bartosak made 23 saves in a 3-0 victory.