Linköping is affected by covid-19 and was missing five players, including the stars Broc Little and Patrick Russell.
They played with as many as five juniors and thus it was perhaps not surprising that Brynäs went up in a 2-0 lead in the first period.
The first goal was a bit lucky when Tomi Sallinen's shot went through Jonas Junland's club and sailed in over Marcus Högberg in the LHC goal.
The second came when Adam Pettersson picked up the puck and put in a backhand.
Linköping reduced in powerplay through Arvid Costmar, but Brynäs increased again.
Anton Rödin finished a contingent.
With three seconds left of the spirit period, Linköping found the net in numerical superiority again.
Markus Ljungh rounded the goal and scored the goal.
Linköping also caught up all the way.
They picked out the goalkeeper and then Alexander Johansson equalized.
The match went to an extra time where both teams had a chance to decide, but neither succeeded.
Once there, Robert Lantosi decided when he set his second penalty.
- We got what we deserved.
We played well for 30 minutes, but then we lost the game and gave it to them, says Brynäs coach Mikko Manner.
By victory, Brynäs had passed Linköping and moved up to a tenth place which means the round of 16.