He remained on track with a birdie at the 14th after getting up and down from a greenside bunker and, after holing a clutch 12-footer for par at the 15th, he notched another birdie at the par-three 16th where he almost took out the flag with his tee shot.
A day after holing a nine-iron from 167 yards at the par-three 16th on Friday, Kim took dead aim with a seven-iron at the same hole, which measured 190 yards on Saturday. "I saw the bounce, but I never saw it go in".
However, he could only par the final two holes as he signed for an eight-under 64 which left him in third place on 17 under.
It was another highlight shot, but he missed the following birdie putt and his four-shot lead was trimmed to one over Monday qualifier Corey Conners after Saturday's third round at the PGA Tour's last stop before the Masters.
"I'm happy with it", Fowler said of the round.
Charley Hoffman, the 2016 Texas Open victor, moved up the leaderboard with a birdie-birdie-eagle finish and the week's best round of 64.
Ian Poulter finished T-44 at last year's Masters after winning the Houston Open the week before, while Russell Henley won in Houston in 2017 and finished T-11 at the Masters the next week. He won the Waste Management Phoenix Open in February and was tied for second when Keith Mitchell sank a final-hole birdie to win the Honda Classic on the Florida swing.
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The South Korean carded six-under-par 66 for a one-stroke advantage over Mexican Abraham Ancer, Venezuelan Jhonattan Vegas and Americans Chris Stroud and JT Poston. Conners only entered the tournament field Monday, and he's the first golfer to win on the PGA Tour after qualifying on a Monday in nine years.
"I definitely feel like I got good work done heading into next week", Fowler said. "That happens. I hit some good shots out there and made a few putts". "Still didn't hit many fairways, but it felt better, if that makes sense".
Hoffman played flawless golf with five birdies in his 67, the last of them at the 18th securing him second place on 18 under.
At the WGC Dell Technologies Match Play last week, he birdied on the final two holes of his first matchup with Billy Horschel to earn a draw.
"I had more control with my long clubs today", Spieth said.
Moore joined Conners at the top of the leaderboard with an 8-foot putt at No. 16 that was his fourth birdie in five holes. And I've made progress.
Fowler bogeyed his first two holes, part of five on the day. He finished at 20-under 268 for the tournament.