Phoenix tied a season best by winning its seventh straight. Six have been by one goal and four by the score of 3-2.
"We created some good chances and unfortunately we gave up that one at the end, but all in all it was good solid team win for us," Phoenix coach Dave Tippett said. "We played a solid road game. I don't think we made too many mistakes."
Sergei Kostitsyn and Shea Weber had goals for Nashville, but it wasn't enough to give the Predators their fourth win in five games.
After a scoreless first period, the Coyotes struck twice early in the second. Yandle began the scoring with a wrist shot through traffic that beat goalie Pekka Rinne at 3:51.
"I was trying to get it by the first guy, maybe have a screen or a guy there to tip it," Yandle said. "I don't think he saw it. Obviously, if you can't see it, you can't save it."
Pyatt followed less than a minute later when he drove from the right faceoff dot toward the Nashville net before lifting a wrist shot just under the crossbar.
Phoenix captain Shane Doan was awarded a penalty shot 10 seconds into the middle period after he was hauled down from behind by defenseman Alexander Sulzer just inside the Predators blue line.
On the penalty shot, Doan faked a slap shot and then tried to slip the puck between the pads of Rinne, but the 6-foot-5 Finn denied the attempt with a stick save.
"He's so good. It's intimidating when you are coming in on him and he is as confident as he is," Doan said. "I tried to go five-hole. I tried to get him to freeze for a sec."
It was the first penalty shot Rinne faced in his NHL career. Doan has failed on all five of his career attempts.
Kostitsyn cut the Phoenix lead in half with a power-play goal at 6:37 of the second.
With Doan serving a delay-of-game penalty, Mike Fisher sent the puck from the left side in front. Falling to his knees in the low slot, Kostitsyn was able to lift his shot over the shoulder of goalie Ilya Bryzgalov.
"Our guys stayed with them the whole game. There was no quit in our game," Nashville coach Barry Trotz said. "I was disappointed in the way we gave up goals. All three could have been very preventable."
Korpikoski scored the winning goal at 7:32 of the third with a slap shot from the high slot, beating Rinne on the glove side. That made it 3-1, but Weber drew the Predators to within one with a goal in the last minute.
"We had chances there, but couldn't find a way," Weber said. "We have to be able to come back. We let this one slip away, but we've got to move on."
Nashville defenseman Ryan Suter left the game late in the second period after a collision with Doan. The team announced that he sustained an undisclosed upper body injury.
Material from wire services and team media was used in this report.
1 - 0 PHX
2 - 0 PHX
2 - 1 PHX
3 - 1 PHX
3 - 2 PHX