Putnam pulled even with Kuchar with three birdies in the first five holes.
The only other time Kuchar won twice in the same season was in 2013, when he won the Match Play Championship in Arizona in February and the Memorial in early June. Now, he has the meat of the season in front of him.
Kuchar has made only one bogey through 54 holes at Waialae Country Club, and his 18-under 192 was the lowest 54-hole score of his career.
Overlooked for last year's U.S. Ryder Cup team after an inconsistent summer, he hit the ground running in the new season and a win at the Mayakoba Classic in November, the eighth of his career, ended a five-year victory drought.
Keith Mitchell surged into joint third place after making seven birdies in a round of seven-under 63, and joined Chez Reavie on 14 under overall.
Even so, the performance was big for Conner, who narrowly missed a full PGA Tour card a year ago.
Reavie finished T18 at this event previous year.
Marc Leishman, Davis Love III and defending champion Patton Kizzire ended the day level alongside Thomas in 17th place. His 64-65 weekend gave him a tie for seventh, and he now heads off to Singapore with hopes of earning a spot in the British Open.
The four-time Ryder Cup team member won a bronze medal for the U.S. at the 2016 Summer Olympics.
At the 480-yard par-4 first, Garber got on in 2 and missed his par putt from 4 feet, finishing with a 3-putt bogey.
Kuchar and Putnam were in a bunker short of the green on the par-5 ninth. He opened the round with birdies on each of the first three holes. Kuchar came out weakly, but made the 10-foot birdie putt. He holed out for eagle three times from the fairway - a sand wedge from 101 yards on No. 10 at the start of his round; a 9-iron from 149 yards on No. 16, and a gap wedge from 135 yards on No. 6. "I didn't find myself in any trouble". "If I just keep plugging along, I (knew) a good thing (was) going to happen".