Jared Spurgeon took the initial shot from the point that Boldy redirected at the left post for the winner. The forward initially looked to score with 5:24 left of the overtime period, but the goal was immediately called off due to a kicking motion.
Brock Faber had a goal and an assist, Kirill Kaprizov had two assists, and Jesper Wallstedt made 43 saves for the Wild, the No. 3 seed in the Central Division.
Matt Duchene and Mikko Rantanen each had two assists, and Jake Oettinger made 40 saves for Dallas, the No. 2 seed from the Central Division.
The best-of-7 series is tied 2-2. Game 5 will be at American Airlines Center in Dallas on Tuesday (8 p.m. ET; FDSNWI, FDSNNO, Victory+, ESPN2, TVAS2, SN360).
Jason Robertson gave the Stars a 1-0 lead with a power-play goal on a snap shot from the bottom of the left circle at 5:35 of the first period. Duchene had the puck in the slot and passed to Robertson in stride toward the net in the left circle.
Faber made it 1-1 when his wrist shot from the right point deflected off Stars defenseman Miro Heiskanen's left leg in the slot and past Oettinger at 13:52.
The Wild appeared to take a 2-1 lead 18:33 into the second period when Joel Eriksson Ek's attempt outside the left post deflected off Heiskanen and into the net. The goal was waved off because the referee ruled that Eriksson Ek interfered with Oettinger by pushing Heiskanen into the goalie.
Heiskanen put Dallas back in front 2-1 with a power-play goal at 19:25 of the second period, scoring with a wrist shot from the top of the left circle that sailed over the glove of Wallstedt.
Dallas went 2-for-2 on the power play and Minnesota went 0-for-4 (three shots on goal). In a 4-3 double overtime win in Game 3 on Wednesday, Dallas went 3-for-8 on the power play and Minnesota was 1-for-7.
Marcus Foligno pulled the Wild into a 2-2 tie when he controlled his own rebound while falling over Oettinger at the left post and backhanding the puck into the net at 14:40 of the third period.
The Stars played with just five defensemen for half the game after Nils Lundkvist exited after getting clipped in the facial area by the skate of Wild forward Michael McCarron after tripping the Wild forward at 13:15 of the second period.
