Bonino scored on a breakaway off a pass from Fiala to give the Wild a 2-1 lead at 6:03 of the third period.
Fiala made it 3-1 with a power-play goal at 11:10. Eriksson Ek was awarded a goal with five seconds remaining after he was tripped with the Arizona net empty for the 4-1 final.
"We've had a few obviously since the Vegas [Golden Knights] games we've talked about how grindy those games were," Wild coach Dean Evason said. "I gotta reiterate how good the teams are in this league. It's a battle every night.
"The game tonight was hanging in the balance for a long time. It was there for either team if you caught a break or a bounce. It's good that the guys are seeing games like this and obviously having success we can reinforce a lot of things that we're doing to stay patient and positive."
NOTES: Coyotes defenseman Niklas Hjalmarsson was a late scratch and is day to day with an upper-body injury. … Zuccarello extended his assist streak to three games (five assists). He has 18 points (four goals, 14 assists) in his past 14 games, tying for second in the NHL in scoring since Feb. 18. … Kaprizov had an assist on Rask's goal, extending his point streak to three games (four goals, one assist). He leads NHL rookies with 24 points (10 goals, 14 assists). … Minnesota has scored at least three goals in 18 of 26 games (16-1-1 in those games). … Arizona is 1-2-1 on its seven-game road trip.