Trump, who lost 5-4 to the Thai player in the quarter-finals of the Scottish Open earlier this month, risked being forced into another final-frame decider.
But the 2020 winner got the better of a lengthy safety battle in the sixth frame before reeling off a break of 47 to seal a 4-2 win and earn his place in the last eight.
Trump told Eurosport: "I was constantly under pressure from the get-go. The first frame was very important and I managed to steal that one and get into the game.
"I just had to keep battling. I didn't play my best but it's always tough to play your best against Thepchaiya, you're on edge and you've just got to get the job done."
Earlier Ronnie O'Sullivan's search for a first ranking title of the season continued as he crashed out 4-1 to world number 43 Martin Gould at the second round stage.
But Gould's good fortune did not continue as he returned in the evening session to lose his last-16 clash by the same score to Ashley Hugill, a result that sent the York player into the quarter-finals of a ranking event for the first time.
Mark Williams opened with a break of 130 as he reached the last eight with a 4-2 win over Barry Hawkins, while Neil Robertson beat Ryan Day by the same score.
In the early hours of Friday, world number two Mark Selby battled back from the brink to overcome Shaun Murphy 4-3, sealing his place in the quarter-final of the English Open after a tense match that lasted over two hours.
Leading 3-2 and on course to take the next frame, Murphy was rocked when he missed what could have been a match-winning black ball, and Selby took full advantage.
In the sixth frame, Murphy missed match ball when on black, which allowed Selby to come back to the table before eventually clearing the colours to force a decider.
In the last-eight, Selby will meet Ali Carter, who beat former world champion John Higgins 4-2 to reach the quarter-finals earlier in the night, making the highest break of the event so far with 142 in the last frame.
Northern Ireland's Mark Allen also progressed with a 4-1 win over John Astley while Belgian Luca Brecel hit clearances of 94 and 70 in his 4-2 defeat of Welshman Jamie Jones.