The 16-year-old Henderson, from Smith Falls, Ontario, had a bogey-free 2-under 70 to move into a tie for 19th at 1 under. She shot 68 on Friday after opening with a 77.
"I didn't have a very good start Thursday," said Henderson, sixth in the amateur ranking. "The last two days have been good. I made five birdies yesterday."
In the third round, she made an 8-foot birdie putt on the par-4 12th and an 11-footer on the par-4 15th. Older sister Brittany is working as her caddie.
"It's great to have her here with me," Henderson said.
The Canadian Women's Amateur champion, Henderson tied for 59th last year in the Women's U.S. Open and has verbally committed to the University of Florida.
Minjee Lee, the 17-year-old Australian who tops the amateur ranking and is 110th overall, was tied for 27th at even par after a 73. She will be the lone amateur in the International Crown team event in July at Caves Valley in Maryland, representing Australia along with Karrie Webb, Katherine Kirk and Lindsey Wright.
Lee won the Australian tour's Victorian Open in February to take the top spot in the amateur ranking. She also won the 2012 U.S. Girls' Junior, and successfully defended her Australian Women's Amateur title this year.
UCLA's Alison Lee and 16-year-old Lilia Vu were tied for 47th at 3 over. Alison Lee, ranked No. 3, had a 70. Vu, from Fountain Valley in Orange County, shot 73. She won the KNC Champions Juniors Challenge in a playoff Monday to earn a spot in the field.
Su-Hyun Oh, a 17-year-old Australian ranked fifth, was tied for 59th at 5 over after a 73.
Angel Yin, a 15-year-old high school freshman from the Los Angeles suburb of Arcadia, followed at 6 over after a 75. She was on the leaderboard after an opening 68, but fell back Friday with a 79. Yin tied for 55th last year.
Alabama's Emma Talley, Southern California's Annie Park, Clemson's Ashlan Ramsey and 15-year-old Nelly Korda, Bahamas winner Jessica Korda's sister, missed the cut.
Michelle Wie and Lexi Thompson, both former amateur participants in the event, were tied for the lead at 10 under.