The Ducks picked up a critical road win that pulled them into a 2-2 deadlock in the Western Conference quarterfinal series. Anaheim will host Game 5 Friday.
Nick Bonino began serving a 2-minute penalty for delay of game late in the second period of a tie contest and he was still in the box when Perry produced his key goal 1:17 into the third.
Ryan Getzlaf added a goal less than 4 minutes later and Brandon McMillan scored 1:55 after that to give the Ducks a three-goal lead.
Cam Fowler, Saku Koivu and Teemu Selanne also tallied for Anaheim, which never trailed and put up a defensive effort that required Ray Emery to make just 19 saves.
Pekka Rinne gave up six goals on 29 shots before being replaced late in the contest by Anders Lindback.
Nashville overcame an early 2-0 deficit and, after falling behind again, tied it with 5:45 to go in the second on Matt Halischuk's wrist shot.