Three powerplay goals for the home side were the difference between the two teams, with Oscar Möller, Linus Lindström and Filip Sandberg - who also scored an even strength goal - all finding the back of the net in the win.
The Giants' only goal came from Colby McAuley, who scored his second in as many games, as they finished bottom of Group H with one win from their six games, but with plenty of respect after some excellent performances.
An early rush from the home side saw Linus Lindström nearly open the scoring just after the clock had ticked over a minute as he crashed the net and the puck nearly trickled over the line, but Peyton Jones managed to recover just in time to stop it crossing the red paint.
Matt Foley headed to the box for tripping on the play but the Giants saw that penalty out, and they had several chances to open the scoring as Mark Cooper and Will Cullen were both denied by home goaltender Alexander Hellnemo.
But Skellefteå were lethal on the powerplay and when Cooper was given a tripping minor towards the end of the period, home captain Möller capitalised by firing a laser of a slapshot into the back of the net from the left circle at 19:01. (1-0)
The Giants killed off the majority of another tripping call, this time against Will Cullen, to start the middle frame and their penalty kill was rewarded when McAuley made it a tied game at 25:11, his shot from the blue line going through traffic and all the way in. (1-1)
But the tie would last for just over two minutes as Filip Sandberg put the Swedes back into the lead, cutting through the middle of the ice and flicking it over Jones to reclaim their one-goal advantage at 27:30. (2-1)
After failing to score on an Elias Salmonsson elbowing call, the Giants needed to batten down the hatches when Gabe Bast sat for hooking and Ben Lake joined him for holding, and they survived seeing Elias Stenman's tip on Måns Forsfjäll's shot hit the post on the powerplay.
Skellefteå netminder Hellnemo came up with a massive save to deny David Goodwin to keep the hosts' lead at one at the second intermission as Scott Conway set up his captain on the two-on-one break, while a boarding call on Leo Bergström also went unpunished.
But in the final period it was a devastating powerplay that saw the home side ease to victory, with Lindström grabbing their third at 42:21 when he was found in the left circle by Sandberg for the finish after Chad Butcher was sent to the box for hooking. (3-1)
And Sandberg himself rounded off the scoring at 49:47 when Conway was boxed for slashing, the winger forcing the puck home under Jones in a scramble at the crease for the final goal of the game. (4-1)
The Giants had one more chance with the final play of the game to grab a consolation as Cooper found the rebound off Conway's initial effort, but the winger could only hit the post to sound an end to the visitors' European adventures.
The Giants return to domestic league action at The SSE Arena, Belfast this Saturday 15 October vs Coventry Blaze for a Premier Sports Elite Ice Hockey League clash, face-off at 7PM. Tickets are available here.
Images by Saga Westin.