Phoenix won its second straight game. Nashville has dropped six of eight.
With the teams skating 4-on-4, Shane Doan fired a pass from the right circle to Yandle skating through the slot. Yandle corralled the puck and put it past goalie Pekka Rinne for his fourth of the season.
Nashville had tied it 2-2 at 12:53 of the third on Weber's goal.
With the Predators on a 5-on-3 power play, Ryan Suter slid the puck to Weber just inside the left point. Weber's one-timer was deflected by Boyd Gordon, who had moved out to try to block the Nashville captain's shot. The puck changed direction and beat goalie Jason LaBarbera over the right shoulder.
Whitney had given the Coyotes the lead 1:40 into the third.
From below the Nashville goal line, and surrounded by two Predators, Radim Vrbata found Whitney alone in the low slot, from where he fired a one-timer past Rinne.
Whitney's goal came 4 seconds after LaBarbera made impressive back-to-back saves on Nashville chances to keep the game tied at 1.
Pyatt gave Phoenix a 1-0 lead just 9 seconds after the opening faceoff when he got the rebound of Lauri Korpikoski's long shot from the right side and the puck past Rinne.
Hillen tied it with just 10.8 seconds left in the first period.
NOTES: Predators RW Jordin Tootoo served the first game of a two-game NHL suspension handed down Tuesday for charging Buffalo G Ryan Miller on Saturday. ... Nashville LW Sergei Kostitsyn returned after missing two games because of an undisclosed upper body injury. ... Hillen played in his 200th NHL game. ... Yandle played in his 200th consecutive game, the longest current streak for the Coyotes. ... Phoenix won both of its games in Nashville this season. The teams will complete the season series on March 12 in Arizona.