Bjerregaard finished second in Hong Kong three weeks ago and said he was determined to go one better in the penultimate event of the European Tour season.
"It was nice in Hong Kong to prove to myself and to everyone else that I can still compete up there," he was quoted as saying by European Tour.com
"So hopefully I can do that again this week and just come up one place better than last time."
The Dane's Hong Kong performance, where he lost out by one shot to England's Justin Rose, went some way to erasing the agony of a final round 17-over-par 89 at the Alfred Dunhill Championships a year ago when he was playing in the final group.
The world number 178 needs a strong showing this week to ensure a place in the 60-man field at next week's season finale in the United Arab Emirates. He is currently 55th in the Race to Dubai Standings.
Overnight leader Garcia recovered well for a one-under 71 and nine-under 135 total after going bogey, double bogey from the 12th.
He recorded a birdie four at the 15th and produced some good work around the greens to close out his round and finish at nine under, alongside Thongchai, who mixed six birdies with two bogeys under grey and gloomy skies in China.
England's Ian Poulter was a further shot back at eight under after a second straight 68, alongside compatriot Paul Casey (69) and South Korean An Byeong-hun, who carded a 71.
England's Danny Willett shot a 69 on Friday to grab a share of 28th at three-under as he bids to overhaul Race to Dubai leader Rory McIlroy, who is not playing in Shanghai this week.
(Writing by Patrick Johnston in Singapore; Editing by Peter Rutherford)
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