Kapur, who grappled with illness last year, is the best Indian at tied-10th. Also placed at tied-10 with him was Indo-Swede Daniel Chopra, who has been struggling with his form.
Chopra, a former two-time PGA winner, shot 67 with six birdies and two bogeys.
Philippines' Angelo Que, who recovered from a slow start, shared the first round lead with Azuma Yano of Japan on six-under-par 65.
Of the other Indians -- Rahil Gangjee and Chiragh Kumar -- also hit bogey-free shot three-under 68 to be tied-15th.
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S Chikakrangappa and Gaganjeet Bhullar faltered with 73 each at tied-89th, needing to get a low score to make the halfway cut, while Jeev Milkha Singh had a forgetful day with 75, leaving a lot of work to done.
Que opened with a bogey but fought back with seven birdies to tie with last year's runner-up Yano at the USD 750,000 event, sanctioned by the Asian Tour and Japan Golf Tour.
The bubbly Filipino, who is a three-time Asian Tour winner, had a chance to redeem himself after finishing in a share of 11th place in Singapore last week when he double bogeyed the last hole.
Korean star K T Kim, a 13-time champion in Japan, trailed the leaders by one-shot as he shared third place alongside countryman Junggon Hwang and Jbe Kruger of South Africa, who qualified for The Open through the Qualifying Series Singapore last week.