Also the Toshiba Classic winner in March in California, Frost hit his approach shot to 10 feet of the closing hole and two-putted to match Couples' par.
Couples had sent his approach into the bunker at right and his potential birdie putt went just to the left.
"I said to myself, 'If he makes his (putt), I'm just going to have to make mine.' I've been in this match play situation many times before and that's just how I try to envision what's going on," Couples said. "You can't help it if he's going to roll his putt in."
The next round of heavy rain started within a couple of minutes of the end of the round, which opened in the morning with a two-tee start.
John Cook and Esteban Toledo finished three strokes back, while Michael Allen, Russ Cochran and Duffy Waldorf were 12 under.
Cook closed with a 66 and Toledo had a 67.
Couples was seeking a second straight win in a major. He sat out the Senior PGA Championship three weeks ago but won the Senior British Open in 2012.
Frost had come close in a major before but this time managed to nurse his one-stroke lead through the final round. He lost to Tom Lehman in a three-way playoff at the 2010 Senior PGA Championship.
Frost's only bogey came on No. 14 while Couples got his 68 with six birdies and two bogeys.
Couples, who had a 3-footer for birdie on No. 15, left the next hole with a grin after matching Frost's birdie.
His expression turned to a wince when his second shot on No. 17 went far to the right, landing down a steep slope from the green next to the grandstands.
He two-putted for his fourth straight par on the hole and couldn't make up that stroke.