Deslauriers scored off a centering pass from defenseman Kevin Shattenkirk on a 3-on-2 break for a 1-0 lead at 4:09 of the third period.
"I just needed to put it in," Deslauriers said. "It was a great pass."
Gibson made seven saves the rest of the way, including three in an eight-second span of the final minute after the Wild had pulled Talbot for an extra skater.
"He just looks so calm and so square and so big in the net," Ducks coach Dallas Eakins said of Gibson. "I always think, when a goalie is playing really well, he makes big saves look really easy, and that's certainly what he looked like tonight."
Gibson was also tested early. He made seven saves in the first seven minutes and 11 in the first period.
"He certainly dialed in and faced a lot of work here early," Eakins said.
Ducks defenseman Josh Manson and Wild forward Jordan Greenway each was assessed a roughing penalty with 40 seconds left in the first period after they tumbled to the ice. Manson sustained an upper-body injury during the incident and did not return to the game.
Shattenkirk played 29:09, and Anaheim defenseman Hampus Lindholm played 29:07.
The Wild won each of their first two games of the season 4-3 in overtime at the Los Angeles Kings, each time rallying from 3-1 down to start the third period.
"We're trying to score, believe me," Minnesota defenseman Matt Dumba said. "We want it to go in the net. Sometimes it just doesn't happen like that. We have to put our heads down and get to work."
Gibson recorded his 20th shutout in his 290th game with the Ducks, the second fewest games to reach that milestone in Anaheim history behind Jean-Sebastien Giguere (238 games).
Gibson nearly had a shutout on Saturday, but the Vegas Golden Knights scored with 1:22 left in the third period and eventually won 2-1 in overtime.
NOTES: Ducks forward Sonny Milano made his season debut and had an Anaheim-high four shots on goal. … Minnesota forward Nico Sturm drew two minor penalties and had a Wild-high six shots.
