The Coyotes trailed by a goal heading into the third but Lee Stempniak tied it on the power play and Jovanovski completed his big night 75 seconds later.
Jovanovski opened the scoring 1:08 into the contest and he forged a 2-2 tie with a slapshot 1:09 into the second.
They were the first three goals of the seasons for Jovanovski, who is in his 15th NHL season.
Ilya Bryzgalov got the win with 28 saves in the second Phoenix victory in six games.
Pekka Rinne stopped 28-of-32 shots in the loss. The Predators have dropped three straight.