Kapur, who was seventh after the first day, is now one-over 217 after a round that had three birdies, three bogeys and a disappointing triple on par-4 16th hole.
SSP Chawrasia had earlier missed the cut at the end of the second round.
Meanwhile Alex Levy, Li Hao-tong, Wu Ashun and David Howell moved into a four-way lead ahead of the final day.
Li and Wu, the locals at Tomson Shanghai Pudong Golf Club, in the world's most populous city, will have high hopes of a home win after both posted rounds of 69 to climb to eight under par alongside Howell, who had earlier signed for a sparkling 68.
Howell, whose last win came in the Alfred Dunhill Links Championship 18 months ago, followed six straight pars with birdies at the seventh and eighth before holing a curling 40-footer on the tenth for a third gain of the day.
Good approach play set up further birdies on the 11th and 13th holes, but he dropped his only shot of the day at the next after pitching into a bunker.
