The four-times world champion led 6-3 from Wednesday's morning session, but breaks of 121, 112 - in which world number 58 Thepchaiya missed the final red when on for a 147 - and 60 saw him close to 7-6 behind with the Scot one frame clear courtesy of an 81 run in the 11th frame.
But the 14th frame proved the turning point as Thepchaiya missed a red among the balls enabling last year's losing finalist to roll in 77 for an 8-6 lead that quickly became 9-6.
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Thepchaiya pinched the 16th frame after Higgins broke down on the blue attempting to force the respotted black.
But a fine run of 54 in the 17th frame paved the way for Higgins to reach the last 16, and a meeting with Jack Lisowski, who toppled 2015 champion Stuart Bingham 10-7 on Tuesday.
Ryan Day - winner of three ranking events this season - produced the highest break of the tournament so far with a knock of 145 as he finished the session in style with a 6-3 lead over Anthony McGill.
Huge fluke keeps Higgins on for 147 - but he settles for 104
Wednesday 25 April
- John Higgins (5) 6-3 Thepchaiya Un-Nooh
- Mark Williams (7) 10-5 Jimmy Robertson
- Judd Trump (4) 6-3 Chris Wakelin
- Neil Robertson (10) 5-10 Robert Milkins
- John Higgins (5) 10-7 Thepchaiya Un-Nooh
- Anthony McGill (14) 3-4 Ryan Day
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