Englishwoman Hull seized control with four birdies in a six-hole stretch around the turn and led by two shots over Xiyu "Janet" Lin (68) and Thitikul, whose eagle-birdie finish gave her a 67.
Thitikul can go to No.1 in the women's world rankings by winning for the second straight week on the LPGA Tour at Old American Golf Club.
The 26-year-old Hull managed just fine and relied on her putting. That's what she least likes to practise at home, instead preferring to improve through playing as many as 36 holes a day.
"I just feel like the putter was very strong today," Hull said. "When I was home I was working quite hard on my putting because I felt like that's the boringest part of the game to practise.
"I don't practise it as much as I should, so I've been doing like two hours each day and just trying to fix it."
She started on the back nine and with a birdie on the par-5 17th, that sent her on her way to three birdies on the opening four holes of the front nine. Hull finished with two birdies and was at 11-under 131.
Thitikul won last week in Arkansas, and at age 19 can replace Jin Young Ko at No.1 in the world by winning.
She will be no worse than No.2 after this week after Nelly Korda shot 75-72 and missed the cut.
Thitikul has made no secret that Old American doesn't suit her game. She told her team around her at the start of the week she didn't have many expectations.
That could be what's helping her as she tries to think less and react to shots.
She overcame a double bogey on the par-4 ninth hole and put herself in great position for the weekend with a 40-foot eagle putt on the 17th and a closing birdie.
"When I started, like before first round, I just told myself and my manager, my caddie, that make the cut is good enough for me here on this course," Thitikul said.
"It's challenging for me. It's dry and it's run-out pretty much, and it's so many bunkers.
"I don't think too much on the course. That's why I can play well these two days."
Lin led by one after the first round and birdied two of the par 5s.
Lindy Duncan had a 65 and was three shots behind. Jessica Korda had a 66 and was four behind, while Lydia Ko also had 66 and was a further stroke back.
Australian Karis Davidson shot another 70 to be two under for the tournament.
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