The American was one shot behind going into the final round at Concession Golf Club in Florida, but removed all drama with a remarkable run to close with a nine-under 63 on Sunday (Monday AEST).
It started with an eagle on the par-5 seventh. He closed out the front nine with back-to-back birdies to seize control, Â then poured it on with a 35-foot birdie putt up the slope for birdie on the par-3 11th.
He was five-under over that five-hole stretch, then it was a matter of everyone else playing for second. Cink added an up-and-down birdie on the par-5 13th, then rolled in an 18-foot birdie on the 14th.
Ben Crane closed with a 68 to finish alone in second in his Senior PGA Championship debut.
South Africa's Keith Horne, who began the final round with a one-shot lead, couldn't keep up with Cink, carding a three-over 75 to finish in a tie for fifth at eight under.
Cink, who won the 2009 British Open in a playoff over Tom Watson, has yet to have a round over par in his 16 rounds on the PGA Tour Champions. Along with his three victories this season, he has a runner-up finish, with his worst result a tie for sixth.
He finished 19-under 269, missing by one shot the record to par of 20 under by Sam Snead in the 1973 Senior PGA Championship at PGA National.
Australians Scott Hend and Steve Allan each closed with a 71 and tied for third.
