The American ranked 175th in the world needed just 20 putts, reeling off 11 birdies - including six in a row from the fifth through the 10th - at Keen Trace Golf Club.
He had a three-shot lead over Rico Hoey of the Philippines and American Hayden Springer.
Hoey's 64 included six birdies and an eagle from off the green at the par-five eighth - his penultimate hole.
Springer, who shot a sensational 12-under par 59 in the first round of the John Deere Classic last week, rattled in a 20-foot birdie putt at 18 to join him on eight-under - his ninth birdie of the day with just one bogey.
Nine players shared fourth on seven-under 65.
"I've been putting really nice all season," said Coody, whose 61 was three strokes better than his previous tour low, a 64 on Sunday at the John Deere Classic.
"It's kind of a core set, if you keep it in play, keep it in front of you, you have a lot of wedges, you end up with a lot of looks for birdie and it's just one of those days that I saw a ton of putts go in."
His six-birdie burst was a first for him. It started with a 14-foot birdie at the fifth. He followed that with a 19-footer at the sixth and a two-putt birdie from the fringe at the eighth.
He said his hole out from a greenside bunker at the ninth "was probably the best of the birdies."
"I was in the right bunker, had a nice lie on the upslope and I made that."
He rolled in a four-footer for a sixth straight birdie at the 10th, then added birdies at 12, 14, 15 and 18.
Coody still had some mild regret when he considered his birdie at the par-five 15th, where he had a 10-foot putt for eagle but ended up making a two-foot birdie.
"The way things were going I certainly didn't expect to miss it, so when it didn't break into the hole I was a little bit shocked," he admitted. "I just tried to stay patient."
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.
