After an opening round that featured a record 16 games decided in overtime, the trend continued in the second with Whitney sending the capacity crowd home happy when he backhanded the puck past Nashville netminder Pekka Rinne while falling with just under six minutes remaining in the first overtime period.
"I held for a second and then went hard to the net, I was a little bit fortunate on the bounce but certainly we will take that for sure," said Whitney.
"When we're up a goal it seems like we're a little bit tighter than we should be but we hang in there and we're comfortable in overtime we've been there so many times.
"When you have a goaltender like Mike Smith in net it gives you a little bit of a calming effect."
The clash between two teams with defense first philosophies was expected to be highlighted by a goaltending duel between the Predators' Vezina finalist Rinne and the Coyotes' Mike Smith but instead it produced some wide open, end-to-end action.
Smith had to be particularly sharp as the Predators outshot Phoenix 42-24.
"I just stuck with and battled and we found a way to win," said Smith. "We've been through it (overtime) so much in the first round we just stuck with it."
The Coyotes, who have had six of their seven play-off games going into overtime, opened the scoring on a powerplay goal from Radim Vrbata that brought the crowd to its feet.
Vrbata, who led Phoenix in regular season scoring, whipped a shot from close range past Rinne for his first of the play-offs.
The Predators leveled the score on a lucky bounce when the puck deflected off the glass to Brandon Yip, who slammed it into the vacant net when Smith left the crease thinking he would make the play behind his own net.
Phoenix regained the lead early in the second on a goal from Rostislav Klesla but Nashville answered again with Andrei Kostitsyn beating Smith.
The Coyotes took a 3-2 lead into the second intermission when Mikkel Boedker converted a two-on-one before Nashville's Martin Erat converted a power play with less than five minutes to play in the third to force overtime.
Game Two of the best-of-seven series is on Sunday in Glendale.