Khudobin made 14 saves in relief of Bishop.
Bishop was trying to become the fifth goalie to get a shutout in four consecutive games he played since 1929-30, when the NHL implemented forward passes in all three zones. The others were Brian Boucher of the Phoenix Coyotes (five games, Dec. 31, 2003-Jan. 9, 2004), Roy Worters of the New York Americans (Nov. 12-20, 1930), Charlie Gardiner of the Chicago Blackhawks (Jan. 8-15, 1931) and Bill Durnan of the Montreal Canadiens (Feb. 26-March 6, 1949).
Jason Zucker scored, and Devan Dubnyk made 27 saves for the Wild (33-30-8), who have lost three straight and are three points behind the Arizona Coyotes for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"I don't know what to tell you," Minnesota forward Marcus Foligno said. "(We're) trying to play for our lives here. … We don't have enough jam right now. I think that's the biggest thing. You've got to have heart, and we have no heart right now."
The Stars scored three goals in 2:22 in the second period.
Faksa deflected a shot by Blake Comeau at 4:11 to make it 1-0.
Hintz gave Dallas a 2-0 lead at 5:25 with his third goal in two games.
L'Esperance made it 3-0 at 6:33 when he scored his first NHL goal off a pass from Jamie Benn.
"There's really no word for it," L'Esperance said. "It's pretty exciting, as you could probably tell with the way I celebrated. I was pretty fired up."
Zucker got the Wild to within 3-1 when he scored on the rebound of a Pontus Aberg shot on the power play at 9:14. It was the Wild's first power-play goal in 19 opportunities.
Radulov scored into the empty net at 18:42 of the third period for the 4-1 final.
"It was a good team effort," Benn said. "I think we worked our way into the game. We played a smart game, and that was top to bottom, both goalies, good team win for us."
