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The Hamilton-born athlete's previous best time in the event was 15min 19.81sec.
Buscomb said she was not sure if she was going to make it through, but thought there was a chance.
"As the race went on I just tried to keep controlled the whole way. It matters what happens on the line, not two laps out."
Buscomb will compete in the final on Sunday morning (NZ time).
Meanwhile, Maddison-Lee Wesche made her World Championship debut in the women's shot put. The under-20 world champion, who has a personal best of 18.32m, needed to throw 18.40m to automatically qualify for the final or finish in the top 12.
The 20-year-old Aucklander threw 16.55m in the first round and 17.22m in the second, but a no-throw in the third moved her out of contention for the final, placing 25th overall.
- The protest against Portia Bing's disqualification from her 400m hurdles heat was unsuccessful, so she will not be competing in the 400m semifinal. Bing was disqualified for her trail leg not clearing the first hurdle.