With the knife to the throat, Seattle won the must-win game on home ice and thus saved itself in the quarterfinal series of the NHL playoffs.
Seattle Swede Alex Wennberg recorded an assist after playing forward Jordan Eberle who shot 6-3 in the open box at the end of the third period, which was also the game's final score.
Eberle was himself a two-goal scorer and was also noted for an assist.
The seventh decisive game of the best-of-seven series will be played in Dallas on the night of Tuesday, Swedish time.
The winner advances to the semifinals and faces either Vegas or Edmonton. Vegas leads its series 3-2 in games and could decide with a win in the sixth meeting on Monday night.