The Wild lead the best-of-7 series 3-2. Game 6 is in Minnesota on Thursday.
Mats Zuccarello scored in his return from injury, and Matt Boldy had a goal and an assist for the Wild, who are the No. 3 seed in the Central Division. Jesper Wallstedt made 20 saves.
Miro Heiskanen and Jason Robertson each had a goal and an assist for the Stars, who are the No. 2 seed in the Central. Jake Oettinger made 24 saves.
Zuccarello, who missed the previous three games with an upper-body injury, gave Minnesota a 1-0 lead at 3:51 of the first period when he scored at the back door after Dallas defenseman Tyler Myers turned the puck over inside the blue line. Kaprizov gathered his own rebound to the left of the crease and passed across to Zuccarello, who swept the puck underneath the stick of Myers and into the net.
Heiskanen tied it 1-1 with a power-play goal at 8:58. He scored on a one-timer from the point, beating Wallstedt between his glove and pad.
Boldy had a goal overturned at 19:47 when Dallas challenged for goaltender interference, but he later gave Minnesota a 2-1 lead on the power play at 19:28 of the second period by scoring from the top of the right face-off circle.
Michael McCarron extended it to 3-1 at 7:47 of the third period. He skated onto a pass from Yakov Trenin in the right circle, moved in on Oettinger and scored through the five-hole.
Robertson cut it to 3-2 at 16:39 when his shot from a sharp angle on the left side banked in off Minnesota defenseman Jared Spurgeon with Oettinger pulled for the extra attacker. Robertson has scored in all five games of the series (five goals).
Kaprizov scored into an empty net at 18:00 for the 4-2 final.
Minnesota defenseman Jonas Brodin left the game at 1:44 of the second after blocking a Mikko Rantanen shot.
Dallas forward Arttu Hyry exited the game at 8:02 of the second with a lower-body injury.
