The 45-year-old, who is looking for his first tournament victory since lifting the Claret Jug at Royal St George's in 2011, was tied with China's Liang Wenchong, who shot a 70 in his third round for an eight-under total.
The Northern Irishman struck five birdies and one bogey on the Montgomerie Course, designed by his former Ryder Cup team mate Colin.
The duo are two clear of South Korean Kwon Sung-yeol (67), Australian Scott Strange (69) and China's Zhang Xinjun (72) with former U.S. Masters champion Charl Schwartzel a further shot back after matching Clarke's 68.
"I've practised really hard these last couple of years since I've won the Open and just not been able to get the scores," Clarke was quoted as saying by OneAsia.
"Obviously I'd be delighted to win tomorrow, but there's 18 holes of golf to go and a lot of talent there or thereabouts at the top of the leaderboard."
Defending champion Liang followed up his 64 in the second round with five birdies on Saturday to leave him paired in the final group on Sunday with Clarke - the winner of two World Golf Championships and 14 European Tour events.
"He is a very respected player and as the local I'm ready to face his challenge and will try my best to play well," Liang said.
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