WATCH: [All Blackhawks vs. Coyotes highlights]
Bouma's first goal of the season came off a scramble in the slot. Tommy Wingels scored an empty-net goal at 19:00 to make it 4-2 and give Chicago's fourth line two goals.
"I think what they did prior to that put them in a position to be out there in that situation, and I like what we saw," Blackhawks coach Joel Quenneville said of the line of Bouma, Wingels and John Hayden. "Those are the kind of goals you score in our league, second opportunities, traffic at the net. Moving forward, we can take a page out of what they're doing."
The Blackhawks (5-2-2) have defeated the Coyotes seven straight times and are 9-0-1 in their past 10 against them. Chicago has not lost a regulation game to Arizona since Feb. 7, 2014.
The Coyotes (0-7-1) are off to the worst start in Arizona/Winnipeg Jets history.
"I thought we were confident all game," coach Rick Tocchet said. "A couple little breakdowns and the puck bounces and it goes to their guy. That's the way it's been going the last two, three weeks."