Fifth-seeded Cristie Kerr, however, was eliminated from the competition by fellow American Vicky Hurst.
The field was whittled to 16 with Angela Stanford, Stacy Lewis, Na Yeon Choi and Morgan Pressel among the winners. Two rounds of matches will be played Saturday at the Hamilton Farm Golf Club with the semifinals and finals set for Sunday.
Tseng defeated Futcher 3-and-1 to set up a third-round match with Candi Kung, who ousted Haeji Kang 1-up.
Hurst's win over Kerr came on the first extra hole, on which Kerr suffered a bogey. Hurst will meet Stanford in the third round after Stanford eliminated Eun-Hee Ji 4-and-3.
Jodi Ewart, who surprised defending champion Suzann Pettersen in the first round Thursday, continued her run with a 3-and-1 victory over Sophie Gustafson. Ewart will next face Azahara Munoz, who was a 2-and-1 winner Friday over Hall of Famer Karrie Webb.
In other matches, Stacy Lewis won over Sandra Gal 4-and-3, Sun Young Yoo defeated Jessica Korda 2-up, Pressel took out Inbee Park 3-and-2, and Amy Yang was a 5-and-4 winner over Natalie Gulbis.