Pyatt scored with 3:29 remaining to lift the Coyotes past the Calgary Flames 2-1 on Thursday night, giving the Flames their first road loss in regulation in nearly two months.
"It's definitely a big win for us against that team," Pyatt said. "That's been one of the best road teams in the league."
Petr Prucha also scored for the Coyotes, who won their third straight.
"The first two or three minutes it seemed like it took us a few minutes to get up to speed or recognize the speed that they were going to play," Coyotes coach Dave Tippett said. "We figured out that we'd better play at that speed, too, or we were going to be in trouble."
David Moss had the lone goal for Calgary, which hadn't lost in regulation on the road since a 2-1 defeat at Columbus on Oct. 13. The Flames were 8-0-2 away from Alberta since then.
"We didn't play well enough," Calgary coach Brent Sutter said. "Our work ethic was fine, but we didn't work smart and made too many mistakes."
Pyatt took a pass from Daniel Winnik and skated down the right side before stopping short in the center of the right circle. He took one stride left before beating goalie Miikka Kiprusoff with a wrist shot.
"One on one, you can't let the guy get the shot off there," Flames defenseman Mark Giordano said.
Moss gave the Flames the lead with 1 second left in the first period. He took advantage of the puck bouncing high off Ilya Bryzgalov's pads to the front of the crease, and scored into the open right side of the net.
Prucha tied it 1-1 at 9:40 of the second, bouncing a shot off Kiprusoff's left shoulder seconds after Phoenix defenseman Keith Yandle struck the left post with a slap shot.
"We played well, a real disciplined game," said Bryzgalov, who made 28 saves. "On the road they've been hot, and it's great to get those points against them."
Kiprusoff, coming off consecutive shutouts, stopped 29 shots.
"They came at us and threw a lot at the net," Flames center Craig Conroy said. "You're upset to waste an effort like that from him. Three minutes to go, you've got to get points."
Coyotes D Ed Jovanovski and RW Peter Mueller both missed their second straight game because of injuries. ... The Flames had won four straight and nine of 11 (9-1-1) on the road against Phoenix. ... For the second straight game, the Coyotes held Flames captain Jarome Iginla without a point. Iginla has 30 goals and 48 points in 49 career games against Phoenix. ... Flames LW Rene Bourque returned after missing six games with an undisclosed injury.