However, no players are guaranteed a place in the knockout round, with all 16 groups to be decided when round-robin play concludes at Shadow Creek Country Club.
Boutier downed the United States' Sarah Schmelzel 2&1 and will oppose South Africa's Paula Reto next, with the winner advancing to the weekend. A tie would see Boutier move on.
Both Australians suffered second-round defeats. First-up winner Karis Davidson was beaten 2 up by American Mina Harigae, while Sarah Kemp lost 2&1 to South Korea's Sei Young Kim.
Thursday's final match resulted in the biggest upset, as Switzerland's Albane Valenzuela defeated top-seeded Lilia Vu of the United States 2 up. Vu birdied the par-3 17th to cut her deficit to one hole, but she double-bogeyed the 18th as Valenzuela made par to seal the win.
"Definitely very happy to walk away with a win," Valenzuela said.
"Lilia is undoubtedly one of the best players in the world and made me work for the points.
"She definitely left some putts out there, and I did as well, so we kind of fought till the end, but just happy to come out with a win."
Valenzuela will advance if she can beat the local Lauren Hartlage, while Vu will face Denmark's Nanna Koerstz Madsen in the group's other match.
Second-seeded Brooke Henderson was beaten 1 up by Sophia Schubert. In a wild match that saw the players halve just five holes, Canadian Henderson fell behind by making bogey on No.17.
"I knew going into it it was going to be a really good match," Schubert said.
"Brooke is an incredible player. She's a really tough competitor. So I just thought, you know, stay patient. It's going to go back and forth all day, but that is OK."
Schubert and South Korea's Jeongeun Lee6 share the Group 2 lead ahead of Henderson and Yaeeun Hong.
In addition to Boutier and Valenzuela, the other players who remain unbeaten are Thailand's Pajaree Anannarukarn, Japan's Ayaka Furue, Ireland's Leona Maguire, Sweden's Maja Stark, Spain's Carlota Ciganda, Americans Cheyenne Knight and Ally Ewing and Sweden's Anna Nordqvist.
The 64-player field is divided into 16 groups with the winner of each advancing to single-elimination play.
Eight matches will be played Saturday morning, followed by four quarter-final matches in the afternoon. The semis and championship match will be contested on Sunday.
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