Linköping had started the season with three straight victories before Friday night's match against Brynäs in Gävle.
Brynäs had the lead twice in the first period.
This after 1-0 from Lara Stalder and also Denisa Krizova who put 2-1.
But Linköping stood for a good match and turned the match fairly during the middle period.
Olivia Zafuto equalized and Madelen Haug Hansen completed the turnaround.
Only with seven minutes left of the third period did Gävlelaget's equalizer come to 3-3 when Josefin Bouveng scored his seventh goal in six games, this time in powerplay.
The American decided
The match in extra time where we only got to see a finish on goal before it was all over.
The puck into Brynäs zone, but had it not been for Olivia Zafuto's sacrificial defensive play, it could have ended differently.
A Brynäs player was close to free kicking when Zafuto threw himself forward and broke the pass.
Shortly afterwards, the puck had instead landed at Justine Reyes who coolly found a gap on Brynäs goalkeeper Ellen Jonsson and scored her second goal of the match.
Linköping won 4-3.
Two points that make you hook on Luleå and Brynäs at the top of the SDHL table.