Reavie shot three straight bogeys through holes 11 to 13 but recovered with seven birdies for a round of 66.
"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. He then reeled off two more over the first three holes after making the turn to regain the lead.
Both courses require keeping the ball in play, and Kuchar has done that well over three rounds. I anticipate shooting another good score tomorrow.
The world number 32 said the quality of his play had been a little better on Thursday, even if his scores had been the same.
The 40-year-old four-time Ryder Cup team member - who won a bronze medal for the United States at the 2016 Rio Olympics - won for the second time in the 2018-19 season after his victory in the Mayakoba Classic in November.
Putnam, who played college golf at Pepperdine and claimed his first PGA Tour victory previous year in the Barracuda Championship, capped his 67 with an eight-foot birdie putt on the last hole.
Kuchar seized control late in the round with back-to-back birdie putts, the second one on No. 16 prompting a rare show of emotion with a fist pump.
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Putnam made his only mistake with a 9-iron into a deep bunker left of the 14th green, leading to bogey.
The win for Kuchar came amid Saturday-night allegations from current PGA Tour Champions player Tom Gillis, who tweeted that Kuchar paid a local fill-in caddie just $3,000 for his Mayakoba win.
Kuchar was sliding his way out of the top 50 toward the end of previous year, when he failed to make a Ryder Cup or Presidents Cup team for the first time since 2009.
Kuchar's final-round 66 put him at 22-under 258 for the tournament, with Putnam finishing at 18 under with a 2-under 68 on Sunday. "I just couldn't keep up with him". It was nice to have that pressure and be able to come through and make some birdies coming.
Corey Conners of Canada, who got into the field through a Monday qualifier, had a 64-64 weekend and was among four players who tied for third, though none had a serious chance of challenging what amounted to a two-player race at the top. "I feel like I was trying to win the tournament trying to make the cut, which is not something I want to get used to".
Andrew Putnam took the lead over Kuchar as the two began their third round as the one-time PGA Tour victor impressed.