Brad Ott is alone in fifth place at 10-under-par, followed by Aaron Baddeley (68), Todd Barranger (69), Stan Utley (69) and D.J. Brigman (69) at minus 9.
Overnight leader Scott Sterling struggled to a 1-over 73 and is tied for 10th at 8-under-par.
Stiles broke into red figures early with three birdies at the start of his round, the farthest from eight feet. He added a five-foot birdie putt at the seventh and closed his front nine with a 15-footer for birdie.
Stiles, a two-time winner on the Buy.Com Tour, drained a four-foot birdie at the par-5 10th and cashed in on a three-footer for birdie at 14. He knocked a 7-iron to two feet at No. 17 to set up birdie then parred the last to match the course record of 64.
The 29-year-old equaled the record set by Chris Smith and Don Reese in 2000. Heath Slocum, Patrick Burke and Skinner shot the number in last year's event.
'I knew after the way I hit it the first two days that if I could get some putts to fall, I could shoot a round like I had today,' said Stiles, who has made just four cuts this season but registered top-15 finishes in all four. 'I just want to go out tomorrow and keep making good swings.'
Caron climbed up the leaderboard on his front nine Saturday with six birdies, including a pair of 15-footers at eight and nine. He made only one birdie on the back, a 10-footer at 14, but that was enough for a 7-under 65.
'There was very little wind today,' said Caron, who tied for 30th two weeks ago at the U.S. Open. 'The golf course is great, but it is a little soft and slow, and that leads to some pretty good scores.'
Sheehan tallied five birdies and one bogey on the front nine to get to 11-under-par but it was his lone birdie on the second nine that tied him for the lead. He roped a 5-iron to 10 feet at the 212-yard, par-3 16th to complete his 67 and join Stiles and Caron in first place.
'I played solid but didn't hit it close on the back nine,' said Sheehan. 'Anybody in the tournament who made the cut had a chance today.'
Full-field scores from the Knoxville Open