Clarke's 1-under 69 was one of only three sub-par performances Saturday on the windy, rainy Royal St. George's course in Sandwich, England.
He drained three birdies and had only a pair of bogeys, finishing 54 holes at 5-under 205. Clarke, looking for his initial major championship, is the only player with three rounds in the 60s.
Dustin Johnson, meanwhile, made the final group for the third time in the last six majors, carding a 2-under 68 to grab sole possession of second place at minus-4.
Johnson is also looking for his first major tournament victory.
Rickie Fowler earned the day's other sub-par round, checking in with a 2-under 68.
That was good for a third-place tie at 2-under 208 with Thomas Bjorn, who registered a 1-over 71 in round three.