Last year's Playoff finalists had been in sparkling form and that looked set to continue this evening when they went ahead as early as the fourth minute through Saku Salminen.
The one-goal advantage and other results going their way meant that deep in the third period the Lappeenranta side were set to climb to first place for the first time this season.
However, that all changed with just 11 seconds of regular time remaining, as Juuso Puustinen clawed out an equaliser for JYP.
Taking all the momentum into the extra period, it was the Jyvaskyla side who grabbed the winning goal, which arrived in the third minute, courtesy of Trenton Bourque, to make it 2-1.
Those two late goals meant SaiPa dropped back to third, while JYP stay second after back-to-back victories.
Despite JYP's win, there was no catching Assat, who remain as league leaders but are now a point clear after coming from behind in a 2-1 win over Vaasan Sport, who dropped into the bottom two.
A second loss in as many matches for Assat looked to be on the cards when Johan Sundstrom gave the home side the lead in the first period, but an equaliser late in the second from Jan-Mikael Jarvinen and a winner in the third from Roope Talaja gave all three points to the Pori side.
Climbing up the table and rounding out the top four are Lukko, who earned a controlled 5-2 away win over KooKoo, while at the other end of the table, Ilves remain bottom despite a 4-3 overtime victory against TPS Turku.
4-3 after the extra period was also the result in Espoo, where Kiekko-Espoo leapfrogged Tappara to go fifth. After a positive start, it's now four defeats in five for the Tampere side, who sit sixth.
One goal was enough for Pelicans to stay clear of the Playout zone and beat Jukurit. The Lahti team are now only two points behind Hameenlinna, who still occupy the final Playoff place despite a 5-2 defeat against Karpat.
Follow Flashscore for all the Liiga results, stats and standings.