Knox was the only player who did not complete the third round on Saturday.
The 30-year-old Scot resumed at the par-five 18th at Sheshan and picked up a stroke to card four-under-par 68.
Knox and American Kisner headed a crowded leaderboard at 16-under 200, one stroke ahead of American Dustin Johnson and China's Li Haotong.
Li, 20, whose father is serving as his caddie, is seeking to become the youngest winner of a World Golf Championships event.
American Jordan Spieth, the Masters and U.S. Open champion, was among a trio three shots back after a sparkling 63 as he bids to return to the top of the world rankings above Australia's Jason Day.
Kisner, 31, has finished runner-up three times in the United States this year.
"I will always use that as motivation to win," he told reporters.
"I played good today. The weather was difficult but I hung in there and made some birdies coming in to give myself a chance to be leading."
Knox, ranked 85th in the world, has not won a tournament on the U.S. circuit, where he mostly plays.
(Reporting by Ed Osmond in London and Andrew Both in Cary, North Carolina; Editing by Ken Ferris and ......)
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