Skellefteå started the best according to plan.
Stekhete Max Lindholm thundered in 1-0 in the power play after just over a quarter of the first period, Lindholm's fifth goal in four games.
But Belfast would come again.
Just 16 seconds into the second period Steven Owre was able to equalize in the box, and just two minutes later Sam Ruopp made it 2-1 with a distinctive pull shot after the Skellefteå defense failed to keep up.
Joakim Lindström had a golden opportunity to equalize on a penalty at the beginning of the third, but the goalkeeper saved the shot on the pick-hand side.
Belfast, which so far has not won a game in the CHL, held out until the middle of the third period, when Filip Sandberg was able to equalize.
Then Andreas Wingerli stepped into the action, first making it 3-2 from close range with three minutes remaining, followed by 4-2 in the open box.
The victory means that Skellefteå is ready for the playoffs with two rounds remaining, as Davos also won their match against Czech Trinec.