In 1869, Wyoming's territorial legislature became the first government in the world to grant "female suffrage" by enacting a bill granting Wyoming women the right to vote. The act was signed into law on December 10 of that year by Governor A.J. Campbell. From:
http://wyoming.gov/state/wyoming_news/general/history.asp

Woman elected governor of a state: Nellie Tayloe Ross, Wyoming, 1925. From:
http://www.infoplease.com/ipa/A0194050.html

Inaugurated fifteen days after Wyoming's Nellie Ross, Miriam Ferguson became the second woman governor in United States history.
http://www.tsha.utexas.edu/handbook/online/articles/FF/ffe6.html
There ya go.