Johnston, who led the NHL with 27 power-play goals in the regular season, scored on a deflection from the slot off a shot from the point by Miro Heiskanen for the winner.
Matt Duchene had a goal and three assists, and Jason Robertson and Mikko Rantanen each had a goal and an assist for Dallas, the No. 2 seed from the Central Division. Jake Oettinger made 28 saves.
The Stars lead the best-of-7 series 2-1. Game 4 is here on Saturday (5:30 p.m. ET; HBO MAX, FDSNWI, FDSNNO, Victory+, truTV, TBS, SNP, SNW, SNO, TVAS).
Marcus Johansson, Joel Eriksson Ek, and Michael McCarron scored for Minnesota, the No. 3 seed in the Central Division. Jesper Wallstedt made 32 saves.
Dallas went 3-for-8 on the power play and Minnesota was 1-for-7.
Duchene tied it at 3-3 when he scored a power-play goal on a snap shot from the bottom of the left face-off circle at 10:18 of the third period.
The Stars took a 1-0 lead with a power-play goal at 1:25 of the first period. Robertson skated over the blue line down left wing and led Rantanen, who got behind Matt Boldy, down the slot for the redirection just inside the right post.
Robertson pushed it to 2-0 on a snap shot from the right face-off circle, beating Wallstedt under his left glove at 13:48.
Johansson pulled the Wild within 2-1 with a power-play goal on a wrist shot from the high slot through a screen at 18:20 that deflected in off two Dallas players.
Eriksson Ek tied it 2-2 on a snap shot from the right hashmarks following a tremendous effort by Boldy, who fended off forward Sam Steel, and defensemen Lian Bichsel and Tyler Myers in the left face-off circle before finding Eriksson Ek at 5:00 of the second period.
McCarron scored his first playoff goal in nine NHL seasons to give the Wild a 3-2 lead on a wrist shot from the top of the right circle at 17:25. The goal came seven seconds after the Wild denied the Stars on a pair of power plays, including a 5-on-3 advantage for 41 seconds.
