Kuchar maintained his lead through the back nine as Putnam began to trail by more with a bogey on the par-4 16th. Lahiri's only birdie of the day came on ninth when he landed his third shot to seven feet and holed it for a birdie.
Fellow American Kuchar fell back to second at 17-under with three bogeys and two birdies after nine holes.
Kuchar ended a four-year drought by winning the Mayakoba Classic in Mexico last fall, and there are a few similarities.
Putnam, who played college golf at Pepperdine and claimed his first PGA Tour victory past year in the Barracuda Championship, capped his 67 with an eight-foot birdie putt on the last hole.
But he remained tied fifth - as he started the day - with American leader Matt Kuchar (66) now seven shots in front of him after getting to 18-under 192, the lowest 54-hole score of his career.
Five-time PGA Tour victor Hideki Matsuyama is 10 shots off the lead, tied for 35th, after also shooting a 3-under 67.
Kuchar is 2-2 when he has the 54-hole lead going into the final round. His best season to date probably came in 2013 when he won the Memorial and the WGC-Match Play Championship en route to $5.6 million in earnings.
Before he made the turn, Thomas rolled in a 12-foot putt for an eagle on the 9th hole.
"It was awfully steady, bogey free, the kind of golf I like to play, give yourself enough opportunities, enough will go in". Just needed to make some better swings. 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.
"Kuch is playing well, so I feel like I've got to get out there and make some birdies if it's not too windy", Putnam said.
Putnam, who won the Barracuda Championship last summer and was runner-up to Dustin Johnson at the FedEx St. Jude Classic, moves into the top 50 in the world for the first time in his career at No. 45. However, his bunker shot got the flawless bounce off the green and one more off the flagstick for an impressive ending.
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 look forward to the rest of the year to try and continue to see how great this year can be". He closed with a birdie Saturday to cut Kuchar's lead to just two.