Perry found himself 10 shots out the lead after two rounds, but mounted a steady comeback over the final 32 holes and shifted into high gear Sunday to win going away.
He finished at 13-under-par 267.
Perry, who also triumphed at the Senior Players Championship two weeks ago, became the ninth play in Champions Tour history to win back-to-back majors.
Grabbing sole possession of second place at minus-9 was Fred Funk, who registered a final-round 2-under 68 at Omaha Country Club.
Michael Allen, who held a five-shot lead after two rounds and a two-stroke advantaged after 54 holes, stumbled to a second consecutive 2-over 72, ending in fifth place at 6-under 274.