Brazier was born in Dunedin to an English father and an Irish mother who came in New Zealand with their first child Tony. Her sport career started at five when his two-years-older brother took her in a rugby field and was split between touch in summer and rugby during winter. She was in New Zealand U21 mixed touch team at 14 and in New Zealand secondary schoolgirls team at 15. She also began to play in Alhambra Union rugby in 2003 and Otago Spirit provincial selection in 2004. She entered New Zealand rugby's record books on 2 May 2009, when she scored 64 points - ten tries and seven conversions - for her club in the Otago Metropolitan Women's Premier match against Kaikorai at the University Oval in Dunedin.
Brazier made her international debut against England on 14 November 2009 at Pillar Data Arena, in Esher, when Black Ferns won 16-3. In the second test match played at Twickenham in front of a record crowd of 12500 people Black Ferns was defeated 10-3. She took part in the 2010 Women's Rugby World Cup, playing a key role in the Black Ferns's success in the final against England and becoming the leading point scorer with 4 tries, 11 conversions and 2 penalties. She scored her first try during the match against South Africa thanks to a fine pass by Anna Richards.
After going to coach and play for Clan Rugby in Edmonton, Canada for four months, Brazier got back in New Zealand for the start of Women's NPC with Canterbury. In spite of a good debut with her new team - two tries in a 60-0 win over Hawke's Bay Tuis - and some other victories against Manawatu Cyclones and her former team Otago Spirit, Canterbury failed to reach the final.
On October 2011 she was called by New Zealand head coach Grant Hansen to play three tests against England: a tour concluded with two losts and a draw for Black Ferns and only 5 points for her (a conversion and a penalty).
Brazier was among the nominees for 2009 Steinlager Rugby Awards as NZRU Women's Player of the Year with Carla Hohepa and Victoria Heighway, who finally won. Brazier was also named the Otago Institute of Sport and Adventure's top sportsperson in 2009 and 2010.