Australia came on the charge but again Woodman showed her worth with an important try saving tackle in the corner.
But the highly-fancied Australians kept on coming and after tries to Emilee Cherry and Elia Green looked sure of taking out the match in regulation.
However a fairly simple kick was missed, giving New Zealand a lifeline.
Extra time meant first to score would grab the gold medal and both sides seemed to be feeling the pressure that comes with that, making uncharacteristic mistakes.
Niall Williams came up with a brilliant try saver to save New Zealand again.
Then, one minute into added time during the first extra period, Brazier spotted a gap right down the middle and took three Australian defenders for a gallop.
Try as they might they could not haul in Brazier who fell over the line to clinch gold.
The medal will go somewhat towards alleviating the heartbreak of the 2016 Rio Olympics final where the fortunes were reversed.