Kapur, who had a closing bogey-free eight-under 64 during his win in Taiwan, had no less than 10 birdies besides two bogeys in his 63 today.
With 65-63, Kapur was 14-under for the weekend and was tied second with fellow Indian Gaganjeet Bhullar (67) at 19- under.
Rattanon Wannasrichan (67) totalling 21-under to complete a sensational victory, closing with a four-under-par 67 to win by two shots.
Kapur, chasing for back-to-back wins, sank four straight birdies in his closing five holes to pile the pressure on Rattanon before signing for the day's best score of a 63.
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Kapur and Bhullar tied for second, making it the third event in last four Asian Tour tournaments that Indians had either won or finishes second.
After SSP Chawrasia's win at Hero Indian Open, Kapur won in Taiwan.
Among the other Indians, Jeev Milkha Singh (72) ended tied-32nd, while Shankar Das (70) and Khalin Joshi (70) were tied-42nd.
Shubhankar Sharma (72) was tied-66th, while Himmat Rai (74) and Chiragh Kumar (72) were tied-73rd. S Chikkarangappa (74) and Arjun Prasad (72) were tied-75th.
"The putter wasn't working too well for me on the first three days but it got hot today. I made a lot of putts except for the last hole but it's golf. I made a lot of putts coming in especially so I can't complain. Hats off to Rattanon for being a better player this week!
Bhullar said it was a great finish with two consecutive birdies to grab a share of second place.
"I played well and I thought at the end of the day, I will either win or finish inside top-five. I am very happy with the way I played. It's been very special. I hit the ball well and it was a great week all over.
Thailand's Panuphol Pittayarat battled to a 70 to finish four shots back in fourth place while compatriot Danthai Boonma grabbed fifth on 268 following a bogey-free 66.
The final round of the Thailand Open was delayed for two hours and 45 minutes in the morning due to heavy rain and lightning threats.
Play commenced only at 10am local time.