"This is what I live for in my career – to do what I did today," said Watson, who fell just short in his brave bid to lift the Claret Jug for a sixth time at Turnberry last July. "I don't think I'll have too many more, but I had this one."
The 60-year-old, coming off a win with Jack Nicklaus in the Wendy's Champions Skins Game in Hawaii the previous weekend, closed with a seven-under 65 to finish on 194, 22-under.
It was his 13th Champions Tour triumph and his first victory in 34 career starts in Hawaii on the two tours.
After pushing his drive into the right rough, Watson hit a spectacular second shot with a pitching wedge from 147 yards that rolled 20 feet on the 18th green and stopped four feet from the hole.
Couples, who closed with a bogey-free 64, just missed his 15-foot birdie putt to the left on the final hole. Watson calmly sank the winner and waved his cap to the roaring crowd, ending a memorable duel he dubbed "young kid versus old fart".
"I didn't win last year. That's how I judge my year," said Watson. "If I win a golf tournament, it's a success. So I started off the year with a success."
The 39-time PGA TOUR winner is the oldest Champions Tour winner since Gil Morgan in the 2007 Wal-mart First-Tee Open at Pebble Beach. Last year, there were no winners older than 55, something Watson early in the week said he hoped to "rectify".
Watson, who bagged five birdies on the back nine to add to the 12 he'd collected over that stretch on the first two days, tied Couples for the lead on the 17th by sinking a six-foot birdie putt.
Couples, who was making his Champions Tour debut in the event along with American Ryder Cup captain Corey Pavin, didn't seem too upset with the runner-up finish.
"I had a wonderful time," said the popular former Masters champion.
"I think I was 21-under par and didn't win a tournament. That hasn't happened too many times."