HV71 led three times against its arch-rival in the heated battle for the bottom spot.
Linköping equalized each time.
Then Nick Shore settled the shootout with his second goal of the night.
The victory means that Linköping extended their lead at the qualifying line to six points with four rounds left to play. The team is also only three points away from a playoff spot.
HV71 remains the second-placed team and is four points ahead of Örebro, the closest team above the qualifying line.
HV71 meets newly reigning giant Leksand away in another important bottom-of-the-table meeting on Saturday.
