Fa'amausili is the first New Zealand age group swimmer to go under the 1:01 barrier and was only 0.6 seconds outside the national open record held by Emily Thomas.
"I am really happy with the personal best and I felt really good in that swim," Fa'amausili said.
Australian Minna Atherton broke the world junior record, going under the one-minute barrier in 59.83s.
North Shore 18-year-old Wilrich Coetzee took 0.7s off his previous best to qualify 10th fastest in heats of the 100m backstroke.
Coetzee, who is coached by Thomas Ansorg, clocked 55.84 in the heats to progress to the semifinals.
"I felt better than expected going through in 27.44 and I just wanted to hold on for the back end of the race," Coetzee said.
The fifth World Junior Swimming Championships, staged at the OCBC Aquatic Centre, continue until Sunday.