It is likely to be humid by night with possibility of fog or mist formation over some internal and coastal areas
An inability to birdie the par-five 18th, where he hit a poor third shot, was the only minor complaint Kuchar had after a four-under-par 66 at Waialae Country Club in Honolulu.
He recorded an 18-under 192 total, while Putnam drained a birdie at the last for a 67 to go 16-under.
Fellow American Keith Mitchell matched the day's best score, a seven-birdie 63, to jump into a tie for third with Chez Reavie (66), four shots behind Kuchar, who has made just one bogey through 54 holes.
"It's not often you feel like you know what you're doing with your swing and the ball's reacting the way you want it to and you're able to manoeuvre the ball the way you want," Kuchar told reporters.
"It doesn't happen near as often as most people think."
Accuracy off the tee with his trusty fade on a shortish course has worked a treat for the 40-year-old.
"That's my strength, finding the fairway and around here it's critical. There are so many doglegs and this rough is nasty," he said.
"It was awfully steady, bogey free, the kind of golf I like to play, give yourself enough opportunities, enough will go in."
Kuchar ended a nearly five-year drought when he won the Mayakoba Classic in November, his eighth PGA Tour win, and he said it was a good recent experience to have in the memory bank.
"I anticipate needing another good round tomorrow," he said.
Second-placed Putnam might fancy his chances of overtaking a player whose reputation as a closer is not exactly of the highest order.
Putnam stayed within striking distance without playing his best.
"I didn't hit the ball as well as first two days, so glad the putter was still warm," he said.
"I'm just going to stay aggressive. There's a lot of birdies out there."
It is likely to be humid by night with possibility of fog or mist formation over some internal and coastal areas
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