Minnesota will advance to the Western Conference Second Round for the first time since 2015. The Wild's last series triumph came against the St. Louis Blues in the 2015 Western Conference First Round, when they clinched the series in six games.
Matt Boldy scored two empty-net goals and Jesper Wallstedt made 22 saves for the Wild, the No. 3 seed in the Central Division.
Hughes gave the Wild a 3-2 lead when his wrist shot from the left face-off circle deflected off the skate of Dallas defenseman Ilya Lyubushkin in the slot and past goalie Jake Oettinger at 10:38 of the third period. Boldy then scored a pair of empty-net goals at 18:29 and 19:45 for the 5-2 final.
Wyatt Johnston and Mavrik Bourque each scored, and Oettinger made 16 saves for the Stars, the No. 2 seed in the Central Division. Dallas had advanced to the Western Conference Final in each of the past three seasons.
Hughes' first goal of the Stanley Cup Playoffs gave the Wild a 1-0 lead at 6:23 of the first period. He collected a return pass from Marcus Foligno, drifted through the slot and fired a wrist shot top shelf over the glove of Oettinger.
Johnston made it 1-1 with a power-play goal at 7:01 of the second period. Mikko Rantanen's pass from below the goal line found Johnston in the slot, who put a snap shot past the right pad of Wallstedt.
Bourque gave the Stars a 2-1 lead at 16:08. Taking advantage of a crazy carom off the end boards, Bourque got the puck at the right post and moved it into the slot before putting it past Wallstedt's back side with a wrist shot.
Just 54 seconds later, Vladimir Tarasenko tied it up 2-2 at 17:02. Hughes' shot from the left point prompted Oettinger to move to the right post to make the save, leaving his backside wide open for a diving Tarasenko to finish the second chance on the backhand.