Adam Pettersson made it 1-0 for the guests Brynäs already after five minutes of play.
It then took until the third period before HV71, which came from two straight wins, broke the deadlock.
Big-playing Brynäs goalkeeper Samuel Ersson had to give up five minutes into the last period when the defenders' points king Eric Martinsson fixed 1-1.
The match went to extra time where a somewhat unexpected match hero stepped forward.
Linus Fröberg had not scored a single goal since November 21 - but now he struck.
After 25 matches without goal cheers, he fixed the extra points for the Jönköping team.
- I did not think it was 25 but 15-20 something.
Like damn it was incredibly nice.
It was important for me and important for the team, says Fröberg to C More.
Brynäs leaves the jumbo place in the SHL despite the loss.
Malmö, which just like Brynäs has been hit hard by covid-19, is a new jumbo in the league.