Couturier gave the Flyers a 1-0 lead at 6:54. Travis Konecny took a long pass from Giroux, stepped around Coyotes defenseman Ilya Lyubushkin, and centered a pass to Couturier, who was driving through the slot for a one-timer.
It ended Philadelphia's goal drought at 159:54, dating to when James van Riemsdyk scored at 6:58 of the first period of a 2-1 win at the Vancouver Canucks on Thursday. The Flyers lost 4-0 at the Calgary Flames on Saturday.
"I think we stuck to what we needed to do to win this game," Couturier said. "It wasn't easy. They're a tough team to play against. They're tight, and I think their record doesn't really reflect the kind of team they are. They're in a lot of tight games, so it was important for us to stick with it, and I thought we did a good job doing that."
It was the third straight game the Coyotes entered the third period either tied or within one goal.
"There's a lot of emotion," Arizona forward Barrett Hayton said. "Guys are frustrated. Those three games, you're going into the start of the third period with the chance to win. Obviously, we have to find a way to score those goals and win that 20 minutes. There's definitely lots of frustration, a lot of emotion."