Kuchar walked in a birdie putt on the par-4 15th, and with Putnam in trouble on the par-4 16th, Kuchar put his approach to 11 feet.
He found a bunker on the par-five 18th hole and looked as if he might finish with yet another bogey.
"Boy, to win two out of three events - it's insane to comprehend", said Kuchar, who missed the Tour Championship last year for the first time in eight years but has now taken his tally of US PGA Tour titles to nine.
The 40-year-old is aiming for his second win in three starts on the Tour after claiming the Mayakoba Golf Classic earlier this season.
"I'm feeling a little let down right now", Putnam said after closing with a 68.
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. But he had a good session with his swing coach in Dallas, and it paid off two weeks later on the Gulf side of the Mexican coast.
Putnam, who won for the first time previous year in the Barracuda Championship held opposite a World Golf Championship, did his best to stay in reach. He finished top five in both events, and following his win last fall at the CIMB Classic should be considered one of the players best positioned to break into the upper crust of golf as we head toward the heart of the season.
"Apparently, I need to go buy a lottery ticket today", Reavie said.
"I want to see how great this year can be", Kuchar said.
Kuchar was at 14-under 126, matching the lowest 36-hole score of his PGA Tour career.
Even so, the performance was big for the Listowel, Ont., native, who narrowly missed a full PGA Tour card previous year. Along with his runner-up finish in the Sanderson Farms Championship last fall, he has almost as many FedEx Cup points as previous year when he finished at No. 130. Marc Leishman, Hudson Swafford, Chez Reavie and Corey Conners were T-3 at 17 under.
Putnam, playing in the afternoon, had a bogey-free 65 and was one shot behind.
Putnam picked up two shots on the front nine at Waialae Country Club to hit the front at 18 under. His latest victory gives him nine PGA Tour victories for his career.
Putnam's birdie at the third and a series of solid pars proved enough to take him into the lead, which he maintained at the turn when he matched Kuchar's birdie at the long ninth. He joins Xander Schauffle in the two-win club for this season and now has almost eight months to notch the first three-win season of his long, consistent and successful career.