Kuzma (28) was second last after her first run earned a score of 56.7, but produced a top run in her second attempt including stomping the right five to earn a score of 90.3 from the judges.
A fifth placegetter in the halfpipe at the 2014 Sochi Olympics, Kuzma produced an excellent third run which was given a score of 86.7 - the second-highest score of the day behind her own second run.
Estonian freeskier Kelly Sildaru (12) won the slopestyle on Friday and led after the first round of the halfpipe with an 86.0 run, but had to settle for second after Kuzma's winning effort, and fellow New Zealander Britt Hawes was third with a top run of 71.3.
''I'm really pumped!'' Kuzma told the competition's website.
''I started off the NZ winter with some new tricks and now I'm feeling well prepared for the northern hemisphere winter.''
Beau-James Wells saved his best until last in the men's competition, but his final run was not quite enough to overtake American skier Taylor Seaton.
Seaton ripped the Cardrona halfpipe to shreds with an opening run of 90.3 - the best first-round run, ahead of Jossi Wells who collected an 86.7 with his first attempt.
Seaton edged further ahead with a second run of 93.0, while Jossi Wells came unstuck attempting his last trick, scoring just 39.0 for the second run. Beau-James Wells, meanwhile, put down his safety run to score 78.3, sitting in fourth place.
He then leapfrogged two skiers to jump to second with his final run of 87.0.
