She carded one-under-par 70 and joined American Jessica Korda a shot behind Higa, who sets the halfway pace at six-under 136 at Country Club of Charleston.
American amateur Gina Kim is two behind.
Boutier, 25, recorded her first LPGA Tour victory when she won the Vic Open in Australia early this year.
She had missed the cut in her only two previous U.S. Women's Open appearances.
The cut fell at three-over 145, with 70 players advancing to the final two rounds.
Defending champion Ariya Jutanugarn of Thailand made it through without a shot to spare after bogeying the final hole.
The third round is scheduled for later on Saturday and with good weather forecast for the weekend, the tournament should finish on time late Sunday afternoon.
(Reporting by Andrew Both; Editing by Hugh Lawson)
