Stephenson turned professional in 1973 and won the Wills Australian Ladies Open that year.

Her most productive period was the early 1980s, when she won all of her majors in consecutive years: 1981 Peter Jackson Classic, the 1982 LPGA Championship and the 1983 U.S. Women's Open.

Stephenson continued playing LPGA events throughout the 1990s, but was hampered by an injury incurred during a mugging in Miami in 1990.

Her left ring finger was broken in two places, an injury that still bothers her play in cold or wet weather.

In 2003, she became the first woman to play on the Champions Tour at the Turtle Bay Championship, where she finished in last place.

She was awarded recognition by the Military Order of the Purple Heart in October 2017 for her service to combat wounded/disabled/blind veterans and first responders.