PHILADELPHIA -- Arizona Coyotes coach Rick Tocchet was determined not to get angry after they let another lead slip away. The Coyotes then showed poise and recovered to avoid a dubious NHL record.
Alex Goligoski scored with 14.4 seconds left in overtime, and Arizona overcame blowing a three-goal lead in the third period to defeat the Philadelphia Flyers 4-3 for its first victory of the season.
[WATCH: All Coyotes vs. Flyers highlights]
The Coyotes (1-10-1) avoided setting an NHL record with a 12th straight loss to start a season. They were tied with the 1943-44 New York Rangers, who started with 11 straight losses before tying their 12th game.
Arizona led 3-1 with less than a minute left. But with Philadelphia goaltender Brian Elliott pulled for an extra attacker, Jordan Weal scored with 53 seconds remaining to cut the lead to 3-2.
Video: ARI@PHI: Couturier tips in Giroux's feed to tie game
The Flyers continued to pressure with Elliott on the bench, and Sean Couturier scored his second goal of the game with 16 seconds left to tie it 3-3.
Two nights after allowing two third-period goals in a 4-3 loss at the New Jersey Devils, the Coyotes were staring at another potential excruciating loss.
"I wanted to stay calm," Tocchet said. "Obviously, you're upset because you can't believe that just happened. But we still have some pretty good players for 3-on-3."
After killing a hooking penalty against Jakub Voracek in overtime, the Flyers (6-5-1) allowed an odd-man rush. Max Domi got the puck to rookie Clayton Keller, who passed to Goligoski for a one-timer past Elliott for his first goal of the season.
"It just feels good to get a win," Goligoski said.
Keller extended his point streak to six games with the assist on the game-winner. He has four goals and four assists in that span.
"The whole building thought he was going to shoot and he made a nice play to Alex," said Tocchet, who got his first win as Arizona coach in the city where he started his NHL career and spent 11 seasons as a player. "He's a big-time player and he's 19 years old."
Jordan Martinook (2:20) and Christian Dvorak (7:46) each scored his first goal of the season in the first period to put the Coyotes ahead 2-0, and Brendan Perlini scored a power-play goal at 1:34 of the third period to make it 3-0.
Video: ARI@PHI: Martinook finishes Hjalmarsson's nice feed
"The first two periods I thought were the best two periods they've played all year," Tocchet said.
The Flyers had three shots on goal in the first period and 13 through the second.
Couturier scored a power-play goal at 2:14 of the third period to make it 3-1. His nine goals lead Philadelphia, which has lost three of its past four games (1-2-1).
Flyers defenseman Ivan Provorov had the first three-assist game of his NHL career.
Coyotes defenseman Niklas Hjalmarsson had two assists but left the game at 8:36 of the third period after he was hit in the face by Flyers forward Travis Konecny's stick. Tocchet didn't have an update.
Scott Wedgewood made 28 saves in his Arizona debut. He was acquired in a trade from the New Jersey Devils on Saturday.
"He was solid," Tocchet said. "He looked big in the net. That's what I liked about him. He stopped the shots he should stop."
Elliott made 30 saves for the Flyers, who are 0-2-2 in their past four games against the Coyotes.
"It's pretty frustrating the way we lost," Couturier said, "but at the same time, it's a big point that we didn't deserve at all."
Video: ARI@PHI: Perlini wires wrister past Elliott for PPG
Goal of the game
Goligoski scored with 14.4 seconds left in overtime.
Video: ARI@PHI: Goligoski buries game-winning goal in OT
Save of the game
Wedgewood stopping Weal's shot from in close at 9:01 of the second period.
Video: ARI@PHI: Wedgewood snags Weal's deflection in close
Highlight of the game
Oliver Ekman-Larsson setting up Dvorak's goal at 7:46 of the first period.
Video: ARI@PHI: Dvorak collects point shot, sweeps it home
They said it
"Relief. Excitement. Happiness. You can go on and on with all the adjectives you want. 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." -- Coyotes forward Jordan Martinook
"You have got to love the way we came back. Our third period was our best period by far. We just have to play like that for 60 minutes." -- Flyers captain Claude Giroux
Need to know
Flyers rookie center Nolan Patrick (upper body) missed his third straight game. General manager Ron Hextall said Patrick could skate Tuesday. … Dvorak extended his NHL career-high point streak to four games (one goal, three assists). … Arizona forward Anthony Duclair, who has five points (three goals, two assists), was a healthy scratch. … Three former Flyers played for the Coyotes: Nick Cousins, Zac Rinaldo and Luke Schenn.
Coyotes: At the Detroit Red Wings on Tuesday (7:30 p.m. ET; FS-D, FS-A, NHL.TV)
Flyers: At the Chicago Blackhawks on Wednesday (8 p.m. ET; NBCSN, NHL.TV)
Video: Goligoski's OT winner lifts Coyotes to first win, 4-3