Bader shot a four-under 68 to hold off world number one Yani Tseng after battling strong winds at the Ko Olina Golf Club.
Tseng has won three of the opening six tournaments this season and is already well-placed on three under alongside HSBC Women's Champions winner Angela Stanford, Jiyai Shin and Brittany Lang.
South Korea's world number seven Jiyai said: "This morning my goal was even (par), because it is a pretty tough course and wind makes so difficult.
"My strength is accuracy - I just played simple."
Local hopeful Michelle Wie never recovered from two double bogeys early as she shot a 78 to be 10 strokes off the pace.