Norwegian champions Storhamar had won three and lost three in their Regular Season matches, but Lukko, with four wins and an overtime loss from their six, were the favourites to get a win on the road.
That was not how things were panning out after 40 minutes - late in the first period, a delicate touch from Jacob Berglund deflected Sander Hurrod's centre into the net, before Berglund turned provider for Austin Cangelosi to tap home the hosts' goal number two in the second period.
Things began to go wrong for the hosts when Marcus Bryhnisveen was called for boarding one second into the third period, allowing the Rauma side back into it with a nice finish from Alex Beaucage.
Storhamar not only had a goal disallowed three minutes later, but Lukko equalised within seconds when Steven Jandric poked the puck home from right in front of the net.
With less than three minutes to go, Storhamar were given their second penalty of the period, and again Lukko capitalised, as Eric Gelinas' shot from the blue line flew straight past the tiring home defence to give Lukko the 3-2 win.
Storhamar will have to pick themselves up quickly ahead of the return leg in Finland on Tuesday.
On Tuesday night, Regular Season table-toppers Ilves picked up a narrow 3-2 away win in their first leg against Bremerhaven. Arttu Pelli gave the visitors the lead but back came the German side, with strikes from Alex Friesen and Christian Wejse.
But the match swung with just over two minutes of the second period to play - Bennet Rossmy was penalised for five minutes for boarding, and either side of the break, Matic Torok and Erik Borg scored to turn the game around in Ilves' favour.
The Tampere side will host the "Fischtown Penguins" in the second leg next Wednesday night for a place in the last eight.
It will be all to play for in the second leg in Kuopio next Wednesday after KalPa were held to a rare draw by reigning CHL champions Zurich, as the first leg match finished 4-4 in Switzerland.
KalPa responded well to going a goal behind in the first period and were 2-1 up just over three minutes later, but strikes from Andy Andreoff and Denis Malgin past the midway point in the second period swung the match back in Zurich's favour.
But back came the Finnish club, who equalised through Aleksi Klemetti before Andreas Okany made it 4-3 with under eight minutes to play. However, the Liiga Playoff champions could not hold on, and just over two minutes later, Sven Andrighetto tied things up ahead of a tantaslising second leg.