After a goalless first period, Frolunda turned things up a notch away at Eisbaren Berlin to eventually run out 4-1 winners.
Erik Thorell broke the deadlock within five minutes of the second period getting underway, before Henrik Tommernes and Jacob Peterson put the Gothenburg side in control.
Leo Pfoederl pulled a goal back for the German side late in the second, but they could not eat further into the Frolunda lead, which Thorell increased late on with an empty-netter to round off a 4-1 win.
12 points from five games was plenty for the Swedish club to book their Round of 16 spot, while the Polar Bears sit outside the top 16 with only four points so far.
The other two Swedish clubs in the 24-team competition both find themselves in the all-important top 16 with one round of matches to play, but neither Lulea nor Brynas could pick up points and will likely need something in the final round to be sure of going through.
Brynas were unfortunate not to go ahead inside the first two minutes of their match with Storhamar when Bobby Trivigno's goal was disallowed following a review, and things got worse for the Gavle side with five minutes to go in the first when they fell behind to a Marcus Bryhnisveen strike.
Tyler Vesel's goal in the seventh minute of the third period finally drew the hosts level, only for Colin Campbell to win it 2-1 for the Norwegian club just over four minutes later. Brynas sit in sixth place following Tuesday's matches with three wins and two defeats.
Lulea had won in regulation time two and lost two in overtime in their first four, but they finally tasted defeat within 60 minutes after a 2-0 loss to Bremerhaven, leaving them in eighth place.
Bennet Rossmy put the Pinguins a goal to the good early in the second period, before Jan Urbas settled matters with seven minutes to play. Leon Hungerecker recorded a shutout for the German side, but his evening was made easier by Lulea only taking 12 shots on goal.