American Putnam has sole possession of second place following his first-round 62 at the PGA Tour tournament, while Matt Kuchar (63) is a stroke further back.
Marc Leishman and Hudson Swafford both carded near-identical six-birdie 64s to earn a podium finish on 17 under along with Chez Reavie, who parred the opening 11 holes and birdied three of the last four to salvage a 67.
Kuchar, 40, held a two-shot lead entering the final round at Waialae Country Club, but saw that evaporate with three birdies over his first five holes against a lone birdie.
The victor of the Mayakoba Classic in Mexico in November, world No.32 Kuchar briefly surrendered the lead to Putnam after three bogeys in his first five holes on Sunday. Andrew Putnam grabbed a share of the lead when Kuchar bogeyed Nos. Putnam went first and it rolled out to 2 inches for birdie.
The 25-year-old won the Memorial Tournament, the Northern Trust and the Dell Technologies Championship in 2018, and moved up 30 places after mixing just one bogey with eight birdies, including three in a row on the way back to the clubhouse.
For Kuchar, the victory will probably propel him all the way to the Tour Championship later this season and could even be the start of a career year. Instead, it turned into the American's first top-10 finish since the 2017 WGC-Bridgestone Invitational and his best result since winning the Desert Classic nearly exactly two years ago.
"I loved the fight", Spieth said.
"I feel like my game has turned into a game that can play well at any given course", Kuchar said. He finished strong with two more birdies in his final three holes to remain in contention as he carded a 4-under 66.
I get where he's coming from and know that he's just trying to build confidence, but I might have to amend my "Spieth will win three times in 2019" take in a few weeks.
At the 477-yard par-4 13th, the Indian's tee shot went 269 yards to the right rough, his second shot went 180 yards to the right front greenside bunker, and his sand shot went 29 yards to the green where he secured a two-putt for a bogey.
"Honestly, I didn't think about it at all until after the third one went in", Reavie added.