Three losses in succession had left JYP holding onto fourth place by a thread, so a visit to Ilves - who had lost one of their last 15 and had top-four ambitions of their own - looked to be the worst possible fixture for the visitors.
But a Valtteri Ojantakanen goal in the 14th minute settled their nerves, before Tobias Winberg doubled the lead in the fourth minute of period two. Then, the home crowd were left stunned soon after the midpoint in the match, as they found their side 3-0 down thanks to Daniel Torgensson's strike.
Toni Utunen finally got Ilves on the board in the 10th minute of period three, but that looked to be just a consolation, until a powerplay allowed Lukas Jasek to cut the gap back to one with a little under seven minutes to play.
The Lynx threw everything at JYP in the final minutes, and got their reward with 29 seconds remaining, as Simon Johansson scored to level the scores and send the match to overtime.
Ilves couldn't complete the turnaround in the extra period, but when Matic Torok put them ahead in the shootout, they thought that would be enough. However, Juuso Puustinen had other ideas - he scored two penalties to win the shootout 2-1 and give JYP a stunning 4-3 victory.
Yet, that was not enough for JYP to maintain their place in the top four, as KooKoo dispatched IFK Helsinki 6-1 to replace them in fourth, as JYP fell to fifth, while two losses in three now for Ilves sees them a point further back in sixth place.
Ville Meskanen got the scoreboard ticking for KooKoo just 17 seconds in, and when he scored his second in the 13th minute of period two, that made it 3-0 to the visitors after Vilmos Gallo had found the net earlier in the middle period.
Vincent Marleau gave HIFK hope in the opening minute of the third period, but Miska Siikonen's powerplay goal five minutes later all but ended comeback aspirations, before Ossi-Petteri Jaakola and Manu Makela completed the 6-1 rout late on.
It's six wins in their last seven now for the Kuovola side, with two in a row finishing 6-1 after their thrashing of JYP at the weekend. HIFK stay in 11th place, but will ne looking over their shoulders after two losses on the spin.
SaiPa remain in third place and have drawn level once more with second-placed Lukko, after a 2-1 away success at Karpat, who remain one place off the bottom. All the goals came in the first period, as Henri Nikkanen scoring what turned out to be the winner for SaiPa's fourth win in their last five.
Also winning 2-1 away but needing overtime to do so were KalPa, who sit seventh following a third win in a row as Teemu Hartikainen's goal in the extra period downed Kiekko-Espoo. It's four consecutive losses for the hosts, who are two places but 13 points behind the Kuopio side.