Jordan Kyrou scored four points (two goals, two assists) and Klim Kostin had two goals for the Blues, who have won their first two games this season. Justin Faulk had a goal and an assist, and Jordan Binnington made 22 saves.
"It was a momentum game," Kyrou said. "We had a lot of momentum in those five to 10 minutes. We got a lot of goals in there, which is huge for us."
Clayton Keller had a goal and an assist, and Phil Kessel and Shayne Gostisbehere each had three assists for the Coyotes (0-2-1) in their home opener.
"It's embarrassing … we were talking that when things get tough, we turned selfish," Keller said. "I liked our first period, and then we just totally got away from it. They're a good team and that's what happens."
Carter Hutton allowed six goals on 21 shots and was pulled in the second period. He has allowed 14 goals on 46 shots in two games, including an 8-2 loss to the Columbus Blue Jackets on Thursday. Karel Vejmelka made 11 saves in relief.
Faulk tied it 2-2 on a power play at 11:10 of the second after Hutton lost his stick for the first of the five unanswered goals.
Kyrou, who had 14 goals in 55 games last season, scored unassisted off Ryan Dzingel's turnover at 12:46 to give the Blues a 3-2 lead.
"I want to come in and be an impact player and help this team win," Kyrou said. "The biggest thing for me is playing the right way."
Kostin's first goal, and the second of his NHL career, made it 4-2 at 14:40.
"I saw a lot of skates in front of me, and I just closed my eyes and shot it," Kostin said.