Nick Bjugstad, Denis Malgin and Mike Matheson scored for the Panthers (13-16-5), who went 2-2-1 on their trip.
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"It's been a long trip," Boughner said. "It's been 10 days, and I know the guys are anxious to get home. We found a way to become .500. We could have been a lot better, but tonight we found a way to compete for the last 20 minutes."
Matheson gave the Panthers a 3-2 lead at 5:41 of the third period when he scored the third straight goal for Florida. He got behind Coyotes defenseman Jason Demers before deking goalie Antti Raanta and beating him between the pads.
"Unbelievable goal," Bjugstad said. "I can't believe he did that."
Matheson has three goals in the past five games after he went his first 28 of the season without scoring.
The Coyotes (7-24-5) lost their seventh straight game (0-6-1) and are 1-8-2 in their past 11. Christian Fischer and Derek Stepan scored for Arizona, which has nine goals during its losing streak.
"I'm kind of embarrassed for the fans because we had this game and we gave it to them," Coyotes coach Rick Tocchet said. "A couple of individuals, I don't understand what they're doing on those plays. It's probably as disappointed as I've been in this team all year."