Clarke moved to 8-under 132. Noren, who is seeking his first title of the season, shot a second consecutive 66. Rock had a 64, making four birdies in five holes from the 11th.
Clarkes lowest European Tour round since 1999 put him in contention for a Ryder Cup wild card on Nick Faldos team.
I need to play well this week and next week, and so far this week Ive done that, the Northern Irishman said. If Nick then feels I am worthy of a pick, so be it. If not, then thats acceptable.
Henrik Stenson (65), who has already secured a spot on the Ryder Cup team, and Englishman Ross McGowan (64) were tied for fourth, one shot behind the leaders.
Justin Rose, who is seeking one of the last three automatic spots on Faldos team, was tied for 14th after a 69. Overnight leader Rolf Muntz (72) was also in a group tied at 14th.
The KLM Open and the Johnnie Walker Championship next week in Scotland are the last chances to earn a Ryder Cup spot.