Australia struck first in the opening quarter, but the two sides traded goals in an evenly-matched and high-scoring first period to take the score to 5-5 at the whistle.
The Australians pushed ahead in the second period to forge a two-goal lead, but China responded well and the teams drew the second period with three goals apiece to go into half time at 8-8.
A strong third quarter for China put them two goals clear, going into the final quarter at 12-10, before a dramatic fourth period saw Australia take advantage of a man-up to claw a goal back, and then China converted their own power play to restore their two-goal cushion.
Australia scored two more man-ups to redress the deficit, bringing the score to 13-13 with 90 seconds on the clock.
With just 58 seconds remaining, China captain Teng Fei lobbed into the top corner, but Australia were not out of it yet.
Holly Lincoln-Smith won a foul for Australia on the five-metre line, then flung in an audacious swivelled back-shot with 35 seconds remaining in regular time, sending the Australia fans wild.
In the first of two three-minute periods of extra-time, Australia edged ahead by one goal, winning the period 2-1, but the Chinese reversed the scoreline in the second short period to take the teams to a shoot-out.
Australia were on the back foot after missing their first five-metre throw, with China scoring their first two.
But Australia netted their next four, taking advantage of two misses by China, to win the game.