Defeated 2-1 at home in the first leg of their Round of 16 clash, Brynas had it all to do as they travelled to the Swiss capital, but the job looked halfway done late in the opening period, as they took advantage of a powerplay to go ahead through Jack Kopacka.
However, a three-minute period of dominance from Bern looked to have booked their place in the last eight, as Miro Aaltonen, Hardy Aktell and Joel Vermin all got on the scoresheet to put the hosts 5-2 ahead on aggregate with 30 minutes to play.
Jakob Silfverberg reduced the deficit before the second period was out, and though Kopacka's second goal put Brynas within one, they were running out of time.
That was until 56 seconds left on the clock, when a scramble ensued in front of the Bern goal, and Oskar Lindblom was the man to force the puck into the net, giving Brynas a 4-3 lead on the night and making it 5-5 across the two legs, sending the sides to overtime.
In the third minute of the extra period, Johan Larsson broke out of his own defensive zone, and though Brynas had a two-on-one, Larsson needed no second invitations to drive forward himself and plant the winning goal into the Bern net to win it 6-5 on aggregate for the visitors.
Brynas' comeback meant all three Swedish Hockey League (SHL) sides have made it through to the Quarter-finals, even though they were the only team from Sweden to win tonight.
Frolunda fell to a second defeat in as many games in all competitions as they lost 2-1 at home to Grenoble, but a 3-1 win in the first leg meant they had done just enough for a 4-3 aggregate success.
Lulea were also downed, 5-3 on the road against Kometa Brno in Czech Republic, but a convincing win at home in the first leg means they progress as well, 9-6 on aggregate.
Finland's Lukko were pushed hard in the first leg by Norway's Storhamar before grinding out a 3-1 win, and tonight they needed a strong third period to shrug off their visitors, earning a 5-2 victory on the night to progress.
Tomorrow, Ilves and KalPa will have the chance to join Lukko in the Quarter-finals, which would mean six of the eight places will be taken up by SHL and Liiga teams. Respective opponents Bremerhaven and Zurich may have something to say about that, however.
The only match this evening without Swedish or Finnish involvement saw Sparta Prague beat Zug 3-2, but it's the Swiss side who cruise into the last eight, 8-3 on aggregate.