Kapur, who was tied 10th at the midway stage on Thursday evening, carded an even par 72 with three birdies and three bogeys.
Also making the cut was Jeev Milkha Singh (73) but he slipped from tied 32nd overnight to tied 45th at three-under.
Former three-time Asian Tour No.1 Thongchai Jaidee shot a smart three-under 69 and moved up from tied 53rd to tied 32nd at five-under.
At the top South African Branden Grace produced one of the most unlikely birdies out of trouble to grab a share of the lead after round three.
Grace, already a winner at the Alfred Dunhill Championship this season, was one over through four holes when he drove into trees down the right of the fifth.
With no obvious escape route, Grace snap-hooked a wedge to six feet for the most of unlikely of birdies and then he holed from 20 feet at the next.
He had three more gains in an inward 33 for a 68 and 13 under par total.
That put the 26 year old alongside playing partner Emiliano Grillo, Scotland’s Marc Warren and Austria’s Bernd Wiesberger after a day full of twists and turns at the top of the leaderboard.
Wiesberger led for much of the day after birdieing the second and third, and went two clear when he converted from 15 feet at the eighth.
The Austrian however failed to capitalize on the two par fives that followed.