Fowler extended it to 3-0 at 4:19, scoring 45 seconds into the ensuing power play after waiting for traffic to form in front before taking a wrist shot from the top of the slot.
"When somebody takes a penalty like that on one of our guys, it's up to us as a power play to make them pay for that," Fowler said. "I think it kind of rallied our guys."
Arizona has allowed a power-play goal in eight consecutive games (eight goals on 26 power plays).
"We needed to get one on that power play, for sure," Eakins said. "If they kill that whole five [minutes] off, I think some hope and some belief go back into their bench."
Fowler made it 4-0 at 3:02 of the third period with a one-timer from the slot while Jakob Silfverberg screened Ingram.
Hayton cut it to 4-1 at 10:44, switching from his forehand to his backhand and scoring undefended after intercepting Simon Benoit's no-look pass.
"There was about [a minute] there in the second where we gave up two goals and that broke the game a little bit," Tourigny said. "But we were able to crawl back, we had a lot of fight and the guys never quit."