The 27-year-old Jones is at her third Olympics, having been eliminated in the heats at Beijing in 2008, and making the K-1 semifinals in London four years ago when she finished 14th.
Jones said her surprise Olympic success will further her dream of putting the sport "on the map".
"I was so proud as a Kiwi to see the flag go up," she said.
"One of my goals is to put canoe slalom on the map in New Zealand ... hopefully this will grow the sport in New Zealand.
"I left nothing out there ... I wasn't really thinking anything, I just bared my teeth and went as hard as I could.
"I just have to thank my family and friends back home ... without their support I wouldn't be here. And we had a really good vibe within the New Zealand unit."