Neither team was able to score in the tiebreaker's first three rounds, and Matt Calvert of the Blue Jackets started the fourth by missing wide on a shot.
Brunner then came in on Sergei Bobrovsky, faking to the right side of the crease, but sliding to the left at the last instant, trailing the puck behind him. He was able to tuck the disc between the post and Bobrovsky's outstretched leg for the game-winner.
Jimmy Howard stopped 30-of-33 shots in the triumph.
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