Thongchai, who has won 13 times on the Asian Tour, and is a five-time winner on European Tour, and a three-time Asia No.1, made the cut at the Masters for the first time in three appearances.
It also added another feather in the cap for Thongchai, Team Asia's captain in EurAsia Cup. He has now made the cut in each of the other three Majors.
Asian Tour honorary member Vijay Singh of Fiji also took a share of 37th place alongside Thongchai after closing with a 75 while Korean ace K J Choi signed for a final 71 to take a share of 34th place on 294.
American left-hander Bubba Watson won his second Masters title in three years by posting a 69 to don the green jacket again with a 280 total.
Both Spieth and Blixt are first-timers.