Peters fired a 2 under 70 at the 18-hole qualifier on the nearby Castle Course at St Andrews which sent her into a 14-way play-off battling for 11 places in the fourth women's major championship for 2017.
Playing in fading light, Peters' place at Kingsbarns was secure after the first extra hole when four players - Nicole Garcia, Laura Murray, Laura Sedda and Amanda Linner - all bogeyed the 147-yard par-three 10th.
31-year-old Peters now has a chance to atone for her poor record at the Women's British Open, which features a tie for 56th in 2015 as the only time she has made it to the weekend in six previous appearances.
The Colac native will join Whitney Hillier, Katherine Kirk, Minjee Lee, Su Oh, Sarah Jane Smith and Karrie Webb in a seven-strong Australian contingent when the opening round gets underway on Thursday.
World Golf Hall of Fame member Laura Davies was among those who advanced alongside Peters in the play-off and the English legend will compete in a record 37th Women's British Open.
“I’ve played in the last 36 Opens and have never had to qualify so this is a new experience for me,” Davies said between finishing her morning round and the early evening playoff.
Another high-profile player to progress was 2010 US Open champion, Paula Creamer, who fired a morning round of 4 under 68 to finish in a tie for second behind lead qualifier, Ursula Wikstrom, from Finland, who posted a 67.