With 10 wins in their last 11 matches, it looked as though not even Lukko could slow the SaiPa train, but the regular season table-toppers edged a 3-2 home win in overtime.
It appeared to be more of the same in the first period, when the visitors took the lead in the 18th minute. Miska Siikonen refused to give up the ghost and eventually forced the puck past Joni Ortio.
But the home side drew level approaching the halfway point in the match - Antoine Morand timed a pass to perfection and the arriving Henri Ikonen got himself into the right place to apply the finish.
With just over 10 minutes remaining, SaiPa were in front again when Juuso Heikkila - facing away from goal - spun and took a hopeful shot from distance, which somehow made it through a crowd and in.
Lukko had to go for broke, pulling the goaltender and, with less than two minutes to go, an attacking faceoff was worked back to Eric Gelinas, whose ferocious shot beat Kari Piiroinen and took the roof off Kivikylän Areena.
The Rauma side took the momentum with them into the extra period and used it to full effect - in the fourth minute, the visiting defence struggled to deal with Patrick Khodorenko, and Piiroinen could only poke the puck straight to Karson Kuhlman, who took his chance to secure a precious win.
Lukko must now do the same in Lappeenranta on Monday, to prevent SaiPa from reaching the Liiga Finals for the first time.
In Tampere, Ilves also grabbed a first of a possible three must-win games, beating KalPa 3-1 to also take their series to a sixth match.
Just as in the other match, the first period went the way of the form side, as KalPa took the lead in the eighth minute, when Filip Westerlund played the puck into a dangerous area and Jere Karjalainen deflected it into the net.
Early in the second, the home side hit back, needing only 12 seconds to take advantage of a powerplay with a very similar goal - Simon Johansson's shot pass was diverted past the goaltender by Eemeli Suomi.
But unlike the events in Rauma, there would be no retaking of the lead by the visitors. Instead, powerplays would be KalPa's undoing.
Jesper Mattila was called for tripping ahead of the equaliser, and when he was called for hooking midway through the second, Ilves profited once more when Arttu Pelli had time to pick his spot through a crowd.
Another holding call with two minutes left, this time against Lasse Lappalainen, dealt a blow to the Kuopio side's hopes of a late leveller, and allowed Joonas Nattinen to race away and knock the puck into an empty net.
Ilves travel to the Olvi Areena on Monday for game six, where they look to level the series.