Clayton Keller scored his 37th goal of the season for Arizona. Christian Fischer and Lawson Crouse also connected, with Crouse's goal coming on a power play. J.J. Moser had two assists, and Prosvetov stopped 25 shots.
"Obviously not the position we wanted to be in, it was tough giving up that goal late," said Hayton, who scored in the 3-on-3 OT when he took a pass from Maccelli. Juuso Valimaki also assisted to help end the Coyotes' losing streak at five games.
"It was a rough stretch obviously. It's frustrating not winning so it's good to come back tonight and find a way to win this one," Hayton said. "We've learned so much throughout the year and it's important to stick with it down the stretch and have a good finish."
Adam Henrique scored twice for Anaheim, and Ryan Strome had a goal and two assists. Anaheim, which entered Saturday tied for last in the NHL with Chicago and Columbus at 56 points, hasn't won since beating Columbus at home on March 17.
With Anaheim goalie John Gibson sidelined with an illness, Olle Eriksson Ek was recalled Friday from San Diego of the American Hockey League, where he was 2-13-0 with a 4.81 goals-against average. The 23-year-old brother of Minnesota Wild center Joel Eriksson Ek had been up for eight games earlier this season, but stayed on the bench. He made 33 saves Saturday.
"I think he did the best he could," Ducks coach Dallas Eakins said. "I thought he settled in really well and he should be proud of his performance as well. I'm really proud of how the guys continue to work, how they stick together. This season is a tough one, but we'll all be better for it."
Fischer opened the scoring at 12:12 of the first period, poking a rebound off J.J. Moser's shot past Eriksson Ek.
Seven seconds after Fischer's goal, the Coyotes' Victor Soderstrom was called for tripping and the Ducks cashed in when Henrique scored on a wrist shot from the slot at 14:21. Strome assisted on the power-play goal.
Keller moved closer to Keith Tkachuk's Coyotes record of 86 points by scoring at 9:06 of the second, with Nick Schmaltz and Moser assisting. Keller has 85 points with two games to go.
Anaheim made it 3-2 when Strome scored on a cross-ice pass from Derek Grant in front of Prosvetov at 12:01 of the second period. And Henrique scored his 21st on a power play to tie it up at 5:46, six seconds after Crouse was called for hooking. Strome and Trevor Zegras had the assists, with Zegras getting his team-high 39th assist of the season.
Ducks: Host Colorado on Sunday night.
Coyotes: Host Seattle on Monday night. ------