Kapur is the top Indian, while Arjun Atwal (66) made a sharp move up from 49th to Tied-19th, while Gaganjeet Bhullar (71) slipped from 29th to Tied-47th.
Kapur after bogeys on second and third made up with birdies on fourth and eighth but again dropped a shot on seventh. He turned in one-over 35.
On the back nine, he had three birdies against no bogeys for a fine 33 and finished at 68.
Asian Tour regular Brazel bogeyed his opening hole at the Hong Kong Golf Club but bounced back brilliantly with four birdies to tie overnight leader Cabrera Bello, who scrambled to a 70, on 11-under-par 199.
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England's Tommy Fleetwood fired a 67 for third place, two adrift, in the USD 2 million tournament sanctioned by the Asian Tour, European Tour and Hong Kong Golf Association.
A fine 64, which included an eagle two, pushed Korea's Soomin Lee, third here last year, into tied eighth place with amongst others, Thai star Thongchai Jaidee who rued a cold putter en route to a 69. They are five shots behind the co-leaders.
Starting the day three behind Cabrera Bello, Brazel, 38, was delighted he fought back from a jittery start where he featured in the final pairing with the Ryder Cup star.
"It was fun out there. Started a little nervous but I guess that's the situation you're in. Felt the nerves a little bit at lunch time. Just sort of grounded out," he said.
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