Clarke moved to 8-under 132. Noren, who is seeking his first title of the season, shot a second straight 66. Rock had a 64, making four birdies in five holes from the 11th.
Clarke's lowest European Tour round since 1999 put him in contention for a Ryder Cup wild card on Nick Faldo's team.
"I need to play well this week and next week, and so far this week I've done that," the Northern Irishman said. "If Nick then feels I am worthy of a pick, so be it. If not, then that's acceptable."
The KLM Open and the Johnnie Walker Championship next week in Scotland are the last chances to earn a Ryder Cup spot.