Yandle scored his first goal of the season and the New York Rangers beat Arizona 4-1.
''Getting your first goal of the season (is) always fun, (and) against your old team,'' Yandle said. ''It's nice to get the win.
''That's most important.''
Yandle played for the Coyotes from the 2006-2007 season until he was acquitted by the Rangers last season at the trade deadline.
''I tried not to let it get in my head,'' Yandle said. ''After the first couple of (shifts) it was game time and time to play.''
''We have to be better than what we've been,'' Coyotes captain Shane Doan said.
Hayes broke a 1-1 tie with his second goal of the season at 2:35 of the third period. Smith turned the puck over to J.T. Miller trying to play the puck behind the goal line. Miller found Hayes along the goal line, and the second year center lifted a backhand into the net.
''Brutal play,'' Smith said. ''I heard someone call for it and it didn't happen to be our player. It cost us.
''That's on me. I have to make a better play than that.''
Four minutes later, Yandle's first goal of the season increased the lead to 3-1. With New York on the power play, Yandle fired a shot from the point that found its way into the net.
The first of two regular-season meetings this season also marked the first time Yandle and Coyotes winger Anthony Duclair played against their former teams.
New York acquired Yandle, defenseman Chris Summers and a fourth-round pick in next June's draft for Duclair, a second-round pick in the 2015 draft and a conditional first-round selection in June's draft in a trade last season.
Arizona is paying $2.625 million of Yandle's $5.250 million contract this season. He is in the last year of his deal, and could become an unrestricted free agent on July 1.
Duclair had two shots on goal and a hit in 17:31 of ice time. He was unavailable for comment afterward as he was receiving treatment, according to a Coyotes spokesperson. Arizona coach Dave Tippett said the play of Duclair's line as ''just alright.''
Nash was awarded his first goal of the season when he was hooked by Mikkel Boedker on a breakaway with the Coyotes net empty.
Kreider tied the game at 1-1 midway through the second period. The sequence began with Marc Staal passing to Zuccarello from the defensive zone. Zuccarello carried the puck into the offensive zone before sending a cross-ice pass that Kreider redirected for his first goal of the season.
Rangers coach Alain Vigneault said Kreider's goal was important.
''It was a quick transition; it was a fast-paced goal (and the style of hockey) that we like to play,'' he said.
Despite being outplayed for much of the first period, the Coyotes had a 1-0 lead on Dahlbeck's first goal of the season at 15:34.
New York nearly opened the scoring at the 10:08 mark of the first period. Smith couldn't control Stepan's sharp-angled shot and the puck was loose in the crease. But Smith, Doan, Antoine Vermette and Oliver Ekman-Larsson combined to keep the puck out of the net, despite the presence of Nash in front of the goal. A video review upheld the ruling on the ice.
''We (were) fortunate to come in with a lead,'' Tippett said.
NOTES: The teams will meet next month in Glendale, Arizona. Prior to the game, Arizona announced left wing Matthias Plachta has been assigned to AHL Springfield. The Coyotes had called him up Monday, and he was a healthy scratch for Arizona's 3-2 overtime loss to the New Jersey Devils on Tuesday. ... Stepan played despite having a wisdom tooth removed Wednesday. ... Arizona scratched center Kyle Chipchura and left wing John Scott. New York scratched defenseman Dylan McIlrath and right wing Emerson Etem. ... Coyotes center Martin Hanzel played in his 500th game. ... Matt Harvey of the National League champion New York Mets was at the game, and the MSG crowd gave the right-handed starting pitcher a loud ovation. ... There was a moment of silence for New York City police officer Randolph Holder, who was shot and killed in the line of duty Tuesday night.