Chinese Taipei narrowed to within two points in the final minute but Taylor and Micaela Cocks held their nerve at the free throw line to secure a deserved victory.
Earlier a Cocks three opened the New Zealand scoring but the Tall Ferns were then outscored 17-2 and trailed 21-7 at quarter time - 8 turnovers not helping the cause.
Edmondson and Cocks scored consecutive baskets but the Taipei lead grew to 30-13 with 4 minutes left in the half.
Georgia Agnew came off the bench and provided a spark to initiate a 9-0 New Zealand run. Josie Stockill scored from a baseline jump shot and Cocks converted a reverse layup but the Kiwis trailed 35-24 at the break.
Harmon became the first player into double figures with a pair of baskets and Cocks added a jump shot - 35-30 and the momentum had shifted dramatically.
Amazingly Taipei were kept to just three points in the period as the Kiwis locked in on defence - 38-34 at three-quarter time.
Two baseline jumpers from Purcell tied the scores before a left handed hook shot from Harmon took the Tall Ferns ahead 40-38 and after that they would not be denied.
Wednesday is a rest day ahead of quarter-finals action on Thursday. The time of the game and opposition are yet to be confirmed.
Tall Ferns 59 - Purcell 22/13, Harmon 15/15, Cocks 12, Taylor 4, Edmondson 2, Paalvast 2, Stockill 2
Chinese Taipei 53 - H Bao 12, F Huang 7, Y Wu 7
Tall Ferns Programme:
William Jones Cup / 5-9 July / Taipei - Finished tournament with 4-1 record
Singapore Series / 11-16 July / Singapore - Won series 2-0
Preparation Camp / 18-22 July / Bangalore, India
FIBA Asia Womens Cup (WC Qualifier) / 23-29 July, Bangalore, India
- This story has been automatically published using a media release from Basketball New Zealand