Connor Ingram made 34 saves, and Travis Boyd and Nick Schmaltz scored for the Coyotes (20-28-9), who are 5-0-4 during their point streak, which is their longest since a 12-game run (11-0-1) from Feb. 4-28, 2012.
Arizona has also won four straight at Mullett Arena, where it will play 18 of its final 25 games.
"I think there's been a lot of different things," Hayton said. "We cleaned up some things with a couple of practice days, our power play has been good lately, and we're just dialed in.
"We've done a really good job in here. We have an opportunity to play a lot of home games here down the stretch and we want to keep it rolling."
Boone Jenner had a goal and an assist, and Merzlikins made 22 saves for the Blue Jackets (18-34-5), who were trying to win three straight for the first time this season.
"The last little stretch here, we've played some good hockey. It's details and competitiveness, and we're kind of dialing in on that," Jenner said. "Obviously, when you do that, you're going to get better results."