Shot of the day: Kuchar had already moved back in front, but it was the birdie on No. 15 that really put the trophy within reach.
Davis Love III, who first played the Sony Open in 1986, missed by one shot matching the lowest 72-hole score of his career.
It was a hard day for 11-time PGA Tour champion Spieth, who had four bogeys and just one birdie to be tied for 127th and 12 shots off the pace.
"Listen, the game of golf is not easy", Kuchar said after a 4-under 66 to take a two-shot lead over Andrew Putnam into the final round.
- PGA TOUR (@PGATOUR) January 13, 2019 " rel="noopener noreferrer" target="_blank" tied his career low round of 63. They remained tied with five holes to play when Putnam made bogey from a deep bunker left of the 14th green, and Kuchar made a pair of 12-foot birdie putts on the next two holes to seize control. Putnam birdied No. 18. Five 3s in your first seven holes on the back nine with the tournament in the balance is a nice way to close a two-week stay in Hawaii.
After a drive to the right side of the fairway on the 351-yard par-4 10th hole, Smith had a 100 yard approach shot, setting himself up for the birdie.
Kuchar shot 22-under 258 for the week in Honolulu and overcame a rocky final-round start to lock up the four-shot win.
"It was not at all what I was looking for", Kuchar told Golf Channel of his start. Instead, it turned into the American's first top-10 finish since the 2017 WGC-Bridgestone Invitational and his best result since winning the Desert Classic nearly exactly two years ago.
"I anticipate needing another good score tomorrow, " Kuchar said.
"For not playing well at all and being on the bad end of the draw, to miss the cut by one is reassuring", Spieth said. "I know I can't coast".
In-form Bryson DeCambeau posted a seven-under 63 to be sharing sixth place with Leishman and three others.
DeChambeau's round jumped him up into a nine-way tie for fifth place at 11 under, alongside the likes of Marc Leishman (68) and Charles Howell III (64).
"Honestly, I didn't think about it at all until after the third one went in", Reavie added.
The 25-year-old won the Memorial Tournament, the Northern Trust and the Dell Technologies Championship in 2018, and moved up 30 places after mixing just one bogey with eight birdies, including three in a row on the way back to the clubhouse.