Overton, who is looking for the first victory of his 3-year PGA Tour career, shot a 7-under 65 at the Montreux Golf and Country Club course.
Wie drew criticism from LPGA Tour superstar Annika Sorenstam for competing in another men's tournament after having had no success doing so in her still-brief career.
But Wie turned in a 1-over 73 Thursday that left her tied for 77th place in a field of 132 players. She will likely need to shoot at least even-par Friday to be among the top 70 players who will survive to play on the weekend.
No woman in modern golf history has made the 36-hole cut in a PGA Tour event.
Among those who finished behind Wie in the standings Thursday were Alex Cejka, Jeff Maggert and Scott McCarron, who tied for fifth at last week's Canadian Open.