Bryzgalov's play and second-period goal from Charlie Coyle helped move the Wild (41-26-12) seven points ahead of the Dallas Stars in the Western Conference's wild-card race to the Stanley Cup Playoffs.
"That [game] was the definition of grinding it out," Wild coach Mike Yeo said.
Minnesota is in position to land the first wild card and can clinch a playoff spot with a point Tuesday night against the Boston Bruins at Xcel Energy Center.
A busy road schedule has accompanied the stretch drive for the Wild, who wrapped up a run of nine of 12 games on the road; however, they've gone 5-2-2 in those nine games away from home.
Seven goaltenders have dressed for the Wild this season, but Minnesota has allowed 2.35 goals per game, fifth-best in the League. The Wild acquired Bryzgalov from the Edmonton Oilers for a fourth-round pick on March 4 to supplement a position that has been ravaged this season. Bryzgalov is 6-0-3 with a 1.67 goals-against average and a .929 save percentage with the Wild in place of Niklas Backstrom, Josh Harding and Darcy Kuemper, who are all out of the lineup. He has three shutouts since joining Minnesota.
"What you saw tonight is what we have seen consistently game after game," Yeo said of Bryzgalov. "Just very calm in the net and making a lot of very tough saves look easy."
Injuries have hampered the Jets (35-35-10), who were without nine regulars, including captain Andrew Ladd and forward Dustin Byfuglien. The Jets struggled to generate offense and managed eight shots by the midpoint of the game. The Jets were shut out for the second time this season.
Jets goaltender Michael Hutchinson, who started the season in the ECHL, made 16 saves in his NHL debut.
The Wild broke a scoreless tie at 1:05 of the second period when Coyle snapped a one-timer from the bottom of the right circle that squeezed through Hutchinson's pads for his 12th of the season. Coyle, who is part of the Wild's top line with Zach Parise and Mikko Koivu, has five goals and five assists in his past nine games and extended his scoring streak to four games.
With a lead in hand, the Wild were able to rely on Bryzgalov as they have done since he arrived in Minnesota.
"As long as we play well defensively, we're not really worried about going out and scoring [an insurance] goal right away," Coyle said. "It's kind of a process in us playing our game and just breaking it down. We know that when we do that, the goals are eventually going to come. We play like that defensively and have our goalies playing like that, we feel pretty good.
"[Bryzgalov] has been playing great for us. He made some pretty big stops and kept us in the game and kept us with the lead. It's nice to have a guy like that back there [whom] we have confidence in and I know he has confidence in us. It goes both ways."
But Bryzgalov directed away any praise for his play.
"Team effort," Bryzgalov said. "We played very good, a very good game. The guys played an amazing game. They don't give up much. They keep the game simple for me, let me see the shots. They block a lot of shots."
While the Wild's penalty kill ranks 26th in the League, the Wild killed off all four Winnipeg power plays and have gone four games in a row without allowing a power-play goal.
"I think that there has been sort of a better focus and purpose going out on the ice," Yeo said of the Wild's penalty kill. "They've been really battling and gotten back on the same page of how we're supposed to be going out there and doing the job. Whenever your goalie is giving you performances like that, your penalty kill is going to be better.
"You can win games when you get good goaltending, when you get good special teams. We played a strong, structured game and gave ourselves a chance to defend. You can win games when you're not completely at your best."
When he was not stopping pucks, Bryzgalov also found time to encourage the Winnipeg fans that were serenading him with his first name.
"It kind of has become a good tradition every time I play here," Bryzgalov said with a smile. "I want to show them with my hands [to] get louder. It's a good tradition."
At the opposite end of the ice from Bryzgalov, a veteran of 455 NHL games, stood Hutchinson. Injuries to Ondrej Pavelec and Al Montoya led to Hutchinson's recall in March from the St. John's IceCaps of the American Hockey League, where he was 15-5-1 with a 2.33 GAA and a .923 save percentage.
"Two good things happened," Jets coach Paul Maurice said of Hutchinson. "He looked solid and comfortable and his movements were light. The guys in front of him gave him a chance to get into the game, to feel the game. He gave his hockey team a chance to win the game."
A chance to play in an NHL game capped off a regular season Hutchinson that started with the ECHL's Ontario Reign, where he went 22-4-2 in 28 games.
"It's been a whirlwind-type season," Hutchinson said. "Starting off in the [ECHL], it's not something that you really envision. Everyone hopes to play a game in the NHL every single season, but realistically I didn't think it'd be possible. I'm very fortunate to have been in some good situations, and I was able to play well this year, and I was just happy to get a shot."
Maurice expects that Hutchinson will play at least one of the Jets' final two games this season. After that, Hutchinson is likely to return to the IceCaps for the Calder Cup Playoffs.
"It's amazing," Hutchinson said. "You only get one first NHL game, and this is definitely a special experience. It's nice to know that I can play at this level."