Matt Duchene had a goal and an assist, and Jason Robertson scored for the Stars, who are the No. 2 seed from the Central Division. Nils Lundkvist had two assists, and Jake Oettinger made 28 saves.
Brock Faber scored his first two Stanley Cup Playoff goals for the Wild, who are the No. 3 seed from the Central. Quinn Hughes had two assists, and Jesper Wallstedt made 28 saves.
Dallas evened the best-of-7 series 1-1. Game 3 will be at Grand Casino Arena in St. Paul, Minnesota, on Wednesday (9:30 p.m. ET; TNT, truTV, HBO Max, SN360, TVAS, Victory+, FDSNNO, FDSNWI)
Johnston gave the Stars a 1-0 lead at 8:58 of the first period. His slap shot from above the right face-off circle deflected off Wild forward Danila Yurov and then bounced off the end boards and in off Wallstedt's left arm.
Faber tied it 1-1 at 11:33. He took a pass from Hughes, skated around Robertson in the left circle and cut to the slot, where his wrist shot ramped up and in off Oettinger.
Duchene put the Stars back up 2-1 with a power-play goal at 4:02 of the second period. Mikko Rantanen gained the offensive zone along the right boards and sent a backhand pass to Duchene, who snapped the puck between Wallstedt's pads from in front.
Robertson made it 3-1 at 7:09 of the third period when he tipped Lundkvist's wrist shot from the blue line past the right pad of Wallstedt.
Faber cut the deficit to 3-2 at 9:47, burying a wrist shot from the high slot to the blocker side for his second goal of the game.
Dallas was called for too many men on the ice with 3:44 left in regulation, but Minnesota, which finished 0-for-4 on the power play, was unable to find the equalizer.
Johnston scored an empty-net goal while on the power play at 19:10 to secure the 4-2 final.
