Although they got goals from Steven Owre and Sam Ruopp, and a 23-save performance from netminder Peyton Jones, the visitors would have just too much as two goals from Andreas Wingerli and further strikes from Pär Lindholm and Filip Sandberg secured the win.
The Giants started the game very brightly and after failing to connect on a powerplay when Elias Salomonsson took a hooking call just 37 seconds in, they had two big chances to open the scoring.
David Goodwin's initial effort after turning the puck over in the offensive zone was saved by Gustaf Lindvall and the Swedish international netminder recovered superbly to deny Mark Cooper on the rebound, before David Gilbert hit the post off Ben Lake's pass.
Despite the home side's strong start, Skellefteå would lead at the first intermission as the Giants ran into penalty trouble and, although they played out a tripping call on Cooper, a hooking minor against Mark Garside led to Pär Lindholm ripping home the one-timer from the right circle at 16:17. (0-1)
The Giants started the second period on the penalty kill as Lake was called for hooking, but just 16 seconds into the middle frame they tied it up as Owre turned over the puck in the offensive zone and fired home from the right circle for the shorthanded goal. (1-1)
And only two minutes later they tied things up as Ruopp joined the rush, took the pass from Tyler Soy in the left circle and snapped the finish past Lindvall for the go-ahead goal at 22:20. (2-1)
They could have been three goals ahead when Owre hit the post off another rush, while Cooper had a breakaway chance after both sides saw out penalties - Darik Angeli and Filip Sandberg both taking tripping minors - but Lindvall turned his effort away to keep the deficit at one.
An early chance presented itself for Skellefteå when Will Cullen tripped up Andreas Wingerli on the breakaway to concede the penalty shot, but the Swedish winger was denied by a brilliant save from Jones to maintain the Giants' slender advantage.
Having battled for so long, though, the visitors' equaliser was a hard one to take as the puck made its way to Sandberg in the left circle and the winger was able to get it out from under his skates to shoot low under Jones' pads for the tying goal at 47:50. (2-2)
The Giants played out another penalty kill as Gabe Bast was sent to the box for interference to keep their hopes alive, but Wingerli would deliver the dagger blow with just 2:57 left on the clock as he found a rebound at the crease and forced it into the net for the game-winning goal. (2-3)
Needing two goals to keep their CHL dream alive, Keefe was aggressive in pulling Jones for the extra skater, but Wingerli would round things off with the empty net goal with 1:20 remaining to end the Giants' European dream. (2-4)
The Stena Line Belfast Giants travel to Scotland to take on Jeff Mason’s Dundee Stars on Saturday 8th October. The Giants return to the ice at the SSE Arena, Belfast on Sunday 9th October against Guildford Flames. Tickets are on sale HERE!