Wyatt Johnston, the NHL's leading power-play scorer, became the game's hero when he scored the 4-3 power-play goal 12:10 into the second overtime period.
Dallas thus leads the best-of-seven series 2-1.
The away team took a 2-0 lead in the first period. Minnesota's Swedish players then took charge of the comeback. Marcus Johansson reduced the deficit at the end of the period (his 200th NHL goal), and Joel Eriksson Ek tied the score early in the second period. Jonas Brodin had an assist on Michael McCarron's 3-2 goal.
Dallas' Matt Duchene took the game to overtime with his 3-3 goal in the third period.
