Kuchar led by two overnight and had just one blemish on his scorecard over the first 54 holes, but his customary composure slipped early on the final day at Waialae Country Club as he endured a torrid run of three bogeys in four holes.
The 40-year-old Kuchar ended a almost five-year drought when he won the Mayakoba Classic in November.
Winning the Mayakoba ended a long winless drought that stretched back to 2014.
Marc Leishman (T3): It was a great two weeks in Hawaii for Leishman, too.
The 25-year-old, whose best finish last season was a tie for 39th, was trailing clubhouse-leader Andrew Putnam but leapfrogged him after four consecutive birdies on the back nine and one final one on the par-five 18th hole.
For Kuchar, the victory will probably propel him all the way to the Tour Championship later this season and could even be the start of a career year. Last season, he slipped to 76th, his worst result since being 116th in 2008. "To win two out of three is insane to comprehend", Kuchar said.
He never looks to be under stress, though Kuchar says looks can be deceiving.
Trick-shot Tomic bamboozles Kyrgios with bizarre match point serve
He added: "I know this Australian Open is going to be big as well. and I can do a lot better than I've done in the past". However, Tomic finished the 2018 season on good terms as he won the Chengdu Open file and returned to the top-100.
"It was awfully steady, bogey free, the kind of golf I like to play, give yourself enough opportunities, enough will go in".
"So now being in good shape, it's certainly a nice place to be".
The win for Kuchar came amid Saturday-night allegations from current PGA Tour Champions player Tom Gillis, who tweeted that Kuchar paid a local fill-in caddie just $3,000 for his Mayakoba win. I love golf. Grade: A+. It's a challenging one. "It is the golf I like to play to stay out of trouble", he said.
Australian former world No.1 Adam Scott at seven over (72 and 75) and countryman Cameron Davis (five over) have missed the cut. The Tour rookie is tied for 20th with a five-under 135 total.
Andrew Putnam putted nearly unconsciously for four days until he really needed it the most.
Sabbatini, whose wife is from Slovakia, became a naturalised citizen last week, and hopes to play for that country in the 2020 Olympics in Japan.
Canada's Corey Conners, who got into the field through a Monday qualifier, had a 64-64 weekend and was among four players who tied for third, though none had a serious chance of challenging what amounted to a two-player race at the top.