But she could not break clear of England's Georgia Hall, who sank a 10-foot birdie at the last hole to also shoot 69, and keep the heat firmly on the leader.
Phatlum, who has four runner-up finishes on the LPGA Tour but has never won in nearly a decade of toil, will head into Sunday's final round at 13-under 203.
Hall is alone in second place on 12 under, with former women's world number one Ryu So-yeon of South Korea two shots behind after a 67 that matched the day's best score.
Ryu was in danger of slipping down after two early bogeys, but roared back with four straight birdies from the fifth hole, and picked up three more shots on the back nine.
Australian Minjee Lee and Japan's Mamiko Higa both bogeyed the last to card 71 and slip three strokes off the pace, where they were joined by South Korean Park Sung-hyun (69).
The diminutive Phatlum is a relatively short hitter who has found herself at home at Lytham, where the ball is rolling a considerable distance on the fairways, reducing the advantage that long hitters often enjoy on softer courses.
After 47 bogey-free holes she finally dropped a shot at the par-three 12th, where she found a bunker, before parring the final six holes on another pleasant summer's afternoon.
Phatlum has missed only four fairways and four greens in regulation in an astonishing display of precision that might well have left her wondering why she was not further ahead.
"I got nervous too today so I just tried my best," said Phatlum, who sings songs in her head when she starts to feel pressure on the course.
"It makes me calm down and not get too nervous. It's all Thai songs."
Hall was not at the top of her game, and was happy to remain only one shot behind.
"My long game wasn't quite on it today but I putted very well. I holed a lot of putts," said the gallery favourite, in contention for the second straight year at the Open.
She tied for third at Kingsbarns last year, and expects that she will be better for the experience.
"I think I'll be a bit more relaxed," said the 22-year-old.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Clare Fallon and Pritha Sarkar)
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