PHILADELPHIA -- They blew a two-goal lead in the final minute of regulation, but thanks to some overtime heroics by Clayton Keller and Alex Goligoski, the Arizona Coyotes have finally won their first game of the 2017-18 season.

Goligoski finished off a 3-on-2 by depositing a slick pass by Keller behind Philadelphia Flyers goaltender Brian Elliott with 14.4 seconds remaining in overtime to give the Coyotes a 4-3 victory Monday night at the Wells Fargo Center.

With the win, the Coyotes (1-10-1) avoided the dubious distinction of setting the NHL record of most consecutive losses to start a season.

"Relief. Excitement. Happiness. You can go on and on with all the adjectives you want," said Coyotes left winger Jordan Martinook, who scored his first goal of the season. "Everybody is happy. It's nice to finish a game with a smile on your face, even though we probably want to win games a little easier than that."

The Coyotes held a 3-1 lead with less than a minute remaining in regulation. With Elliott pulled for an extra attacker, Jordan Weal scored with 52.6 seconds remaining, and Sean Couturier tied it with 14.4 seconds to go to send the game into overtime.

That's when, after failing to convert on a power play, Keller froze Elliott by faking a shot and passing the puck off to Goligoski, who scored from below the right circle.

"The whole building thought (Keller) was going to shoot and he made a nice play to Alex," Coyotes coach Rick Tocchet said. "He's a big-time player and he's just 19 years old."

Elliott admitted he thought Keller, who leads the Coyotes with eight goals, was going to shoot.

"You have to play the shot there," said Elliott, who stopped 31 shots and fell to 5-2-1. "We put ourselves in a bad position to have a 3-on-2 and you play it as best you can."

Goaltender Scott Wedgewood (28 saves) picked up the win in his first start for the Coyotes after being acquired from the New Jersey Devils on Saturday in exchange for a fifth-round pick. He had not played an NHL game since March 27, 2016, and had played in only one AHL game this season.

In addition to Goligoski and Martinook, Christian Dvorak and Brendan Perlini also scored for the Coyotes, who lost defenseman Niklas Hjalmarsson to an undisclosed injury midway through the third period. Tocchet said Hjalmarsson is day-to-day.

Couturier scored twice for the Flyers (6-5-1), giving him nine goals, five short of his season total from last season.

"It's pretty frustrating the way we lost, but at the same time it's a big point that we didn't deserve at all," Couturier said. "To get a point like that might be huge at the end of the year, so we will take every point we can get."

Tocchet said he told his players before the game that if they kept playing hard, good things would happen.

"I'm really proud of them," Tocchet said. "I know everybody looks at the record without watching us play, but we should have five or six wins right now and that's what I keep telling the players. They came to play."

Flyers coach Dave Hakstol said he was disappointed in his team's play in the opening period, when they were outshot 13-3 and outscored 2-0.

"In the first period, as a group we were too far below the bar," Hakstol said. "There are certain things we need to establish in our own building and we didn't do that."

NOTES: Arizona G Antti Raanta (lower body injury) sat out his eighth straight game, forcing the Coyotes to recall backup Hunter Miska from the AHL's Tucson Roadrunners. Raanta is practicing with the club and could return to action when the Coyotes conclude their five-game road trip Tuesday night in Detroit. ... Philadelphia D Shayne Gostisbehere (upper-body injury) missed his first game of the season, and C Nolan Patrick (upper-body injury) missed his third straight game. Both are believed to have head injuries. ... The Flyers recalled D Mark Alt from the AHL Lehigh Valley Phantoms. He played his second NHL game on a second pairing with Radko Gudas. ... After several players complained about the condition of the ice in their previous home game, the Flyers laid a new sheet of ice for Monday night's game.