Chris Riley, who held a share of the 36-hole lead, carded an even-par 70 to finish alone in third place at 7-under-par 203. Tiger Woods, a three-time winner of this event, was one shot further back alongside Davis Love III at 6-under-par 204.
Woods jumped out of the gate with a birdie at the opening hole at Firestone Country Club, the site of his three NEC Invitational victories. At the par-4 third, Woods missed the green with his approach but chipped in from off the putting surface for a birdie.
The 27-year-old hit his tee shot to 25 feet at the par-3 fifth and drained the putt to reach 6 under. Woods appeared to have shaken off the remnants of a double bogey at the 18th on Friday, but the top player in the game soon found himself in trouble again.
Woods bogeyed the sixth and collected back-to-back bogeys starting at the eighth to fall back to minus-3.
He recovered on the inward half with three birdies to finish well within reach with one round to play.
'I'm right where I need to be,' said Woods. 'I need to get off to a good start and keep it going this time.'
Clarke, who won the Match Play Championship in 2000, picked up a birdie at the second but found trouble with a bogey at the very next hole.
'We've got a lot of the world's best golfers here, and that's a fair reflection on the golf course,' said Clarke.
The Ulsterman began his move up the leaderboard with back-to-back birdies from the fifth but faltered again with a bogey at the 10th. Clarke countered with a birdie at the 11th and rolled in a 16-foot putt for a birdie at the 13th to take the outright lead at minus-8.
Clarke was soon joined atop the leaderboard by Kaye, but he was able to regain the top spot with a fine play at the par-4 17th. After a tremendous drive, Clarke knocked his second within a foot of the hole for a tap-in birdie.
'I got a few breaks early on,' said Clarke. 'I hit some good shots, but thankfully my short game has been very sharp, and that's what made the difference.'
Kaye was on fire early with birdies on each of his first four holes. He stumbled with bogeys at the seventh and the 10th but responded with a birdie at the 11th.
The 32-year-old added a birdie at the 13th and sank an 18-footer for a birdie at the 16th en route to a round of 65.
U.S. Ryder Cup captain Hal Sutton shot a 68 to join Steve Flesch, Retief Goosen and Brad Faxon at 5-under-par 205.
Reigning U.S. Open champion Jim Furyk was one shot further back at 4-under- par 206 along with Robert Allenby, Vijay Singh and Fred Funk.
Ben Curtis put the finishing touches on a third-round 72 before heading off to get married. The ceremony had been scheduled before Curtis' British Open victory opened the door for the 26-year-old to compete in some of the premier events in the world.
'Life won't change, it'll just be a certificate, that's about it,' said Curtis.
The Ohio native finished 54 holes at three-over-par 213.