Victor Rask and Joel Eriksson Ek also scored for Minnesota, now within two points of Vegas atop the West Division.
Minnesota, 11-2-1 in its past 14 games, has won four straight overall and seven in a row at home.
Phil Kessel scored for Arizona in the second of three straight games between the teams.
Back on the ice for a few seconds after coming out of the penalty box, Bonino, streaking across the center ice logo, took a pass from Fiala and beat Antti Raanta on the breakaway at 6:03 of the final period.
''Sitting in the box, you don't want to be responsible for the penalty that the team gets scored on. Huge credit to the kill, I love being out there on the kill, but it was an awesome job tonight,'' Bonino said.
Arizona was scoreless on three power plays. The Wild have killed off 20 of 21 short-handed situations over the past seven games.
Fiala and Matt Dumba perfectly executed a give-and-go for a tap-in power-play goal by Fiala five minutes later. It was the second goal with the man advantage in 11 games for Minnesota, which converts on a league-worst 8.4% of its power-play chances.
Kessel scored the lone goal of the opening period.
Off a Dumba turnover, Lawson Crouse backhanded a pass from below the right circle, where Jonas Brodin mishandled it for Minnesota. Kessel quickly snuck a shot through the pads of Cam Talbot for his first goal in eight games.
The Coyotes have two goals in three games.
''We're not working in the right areas to be in the offensive zone a lot. We don't have five guys getting on forecheck like they should to break up their breakout,'' Coyotes defenseman Alex Goligoski said. ''They're coming up the neutral zone too easy on us and then we're wasting our energy defending and that makes it hard to generate offense.''
Talbot, who stopped 25 shots in Friday's shutout win, finished with 21 saves. Raanta had 31 for Arizona.
Rask evened the game early in the second with his first goal in 11 games.
Kirill Kaprizov circled behind the net and fed a pass to Mats Zuccarello, whose shot was partially stopped by Raanta. With the puck on the blue paint, Rask poked it in for his sixth goal of the season. He had five in 43 games last season.
Kaprizov, who had eight shots on goal for the second straight game, leads the Wild and NHL rookies with 24 points, including a Friday hat trick. Zuccarello, who has five assists in the past three games, is third on the team with 18 points.
''They seem to find each other and seem to look for each other,'' Wild coach Dean Evason said. ''We bounced around a little bit with center icemen with them. ... For the most part it's been Rasky and his offensive IQ is real high and they're able to create and make plays and obviously have success.''
NOT ENOUGH SHOTS
Arizona was outshot 34-22 and has been outshot in 11 consecutive games and 13 of 14.
''There's some moments we have, we have some guys who are reluctant to shoot the puck,'' coach Rick Tocchet said. ''We have guys who haven't scored in 10 or 12 games. Good players for us, maybe one assist and their squeezing it. When you squeeze the stick, you gotta shoot the puck. You gotta get the greasy ones. That's Hockey 101.''
Arizona D Niklas Hjalmarsson missed the game with an upper-body injury. He is listed as day to day. D Ilya Lyubushkin played for the first time in five games. ... Wild LW Marcus Foligno missed the game. He left Friday's game after getting hit by a slap shot on his lower right leg. The team has provided no update. ... Wild C Marcus Johansson (upper-body injury) practiced Saturday, but missed his 13th straight game.
The teams wrap up a three-game series in St. Paul on Tuesday.
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