Coody clings to lead in Kentucky in search of first PGA Tour title
The 24-year-old rookie, who led by three after the first round and by two after the second, had three birdies and three bogeys on the front nine and had fallen off the pace at Keene Trace Golf Club.
But he rolled in a six-foot eagle putt at the par-five 11th, birdied the par-five 15th and drained a 19-foot birdie at 17 to top the leaderboard on 20-under 196.
He was one stroke in front of England's Harry Hall, who carded a 64, and Rico Hoey of the Philippines, who shot 67.
"The front nine, just a few things didn't go my way," Coody said. "Didn't quite hit it the way I wanted to, left myself in some tough spots.
"But every hole feels like out here you can have a chance at birdie with one good shot, so I just tried to stick with that mindset and luckily some good bounces and some good putts on the back nine got me back in it."
Hoey chipped in for eagle at the 15th then drained a 21-foot birdie putt from off the green at 16 to become the first player to reach 20-under.
He arrived at 18 tied for the lead but hit his tee shot left into hip-high rough and finished with a bogey for a five-under 67 to join Hall on 19-under 197.
"I just kind of rushed the swing on the first tee ball and pulled it left," Hoey said of his first bogey of the week. "It's unfortunate that just one bad swing I made a bogey, but it's golf so I can't complain. I set myself up for tomorrow and we'll see how it goes."
Sam Bairstow had 10 birdies in a 10-under 62 to head a group on 198, tied with fellow Americans Neal Shipley (66) and Johannes Veerman (67).
The top six players on the leaderboard are all chasing a first US PGA Tour title.
The tournament is played opposite the Scottish Open, where the tour's biggest names are tuning up for the final major of the season, the Open Championship at Royal Troon in Scotland July 18-21.