Putnam took the lead over Kuchar as the two began their third round.
"I want to see how great this year can be", Kuchar said. He carded one under overall after rounds of 73 and a much-improved 66 in his first event of 2019.
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.
Kuchar had a 54-hole score of 193 in Mexico, the lowest of his career.
So odd was this round that Reavie made more eagles than birdies, and the one shot that made him think the ball might go in the hole led to a par. But, his standing atop the leaderboard was threatened by one-time victor Andrew Putnam. It hopped into the back bunker, and he missed an 8-foot par putt to lose the lead. But the veteran steadied himself down the stretch, racing past Putnam with a flurry of four birdies in seven holes on the back nine.
He gets another test Sunday, and Kuchar at least is equipped with recent experience.
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"Didn't feel as easy as the first two days", Putnam said.
Canadian Adam Svensson earned a one-stroke lead after round one of the Sony Open in Hawaii, where Jordan Spieth stumbled in his first appearance of the season.
"It was so uncharacteristic of me", Kuchar said, referring to his three-putt and bad wedge on No. 5.
"Andrew was tough. He was battling me, took the lead.it was nice to have that pressure, to have come through and to make some birdies coming in".
Armed with a three-stroke advantage with just two holes remaining, Kuchar held firm and, after a cast-iron par at the penultimate hole, he completed a comprehensive win with his 24th birdie of the tournament at the 72nd hole. "I know I can't coast".
Bryson DeChambeau produced arguably the round of the day, matching his career-low 63 to sit tied among a nine-strong pack in fifth place on 11 under.
"I'm just going to stay aggressive".