It was Brassard's first regular-season hat trick in the NHL.
"It's a special night, but I was just trying to help the team win any way we can … I was just at the right place at the right time," Brassard said. "We were ready to play, we had a plan we executed. It's going to give us some confidence scoring five goals."
Antti Raanta made 27 saves, and Jakob Chychrun had a goal and an assist during a three-goal first period for the Coyotes (13-13-5), who won for the first time in six games (1-3-2).
Adam Henrique scored for the Ducks (9-17-6), who fell behind 5-0 in their fifth loss in six games.
"It snowballed right off the bat. Sometimes, I think, the game doesn't have answers for you," Anaheim coach Dallas Eakins said. "We looked a little hesitant and not full of that speed and support. When that happens, it's a cruel league if you're not on your game right away, and you fall down that far in a game."