The defending champions thought they had gone ahead in the 39th minute but Wang Shuang's effort was ruled out by the VAR.
With the teams tied 0-0 after 90 minutes, China finally got the breakthrough four minutes into extra time through Shao Ziqin.
China had a golden opportunity to add to their lead 10 minutes later but Wurigumula's penalty was saved. They got their second thanks to an own goal from Taiwan's Chen Ying-hui four minutes later.
With the win, China booked a spot at next year's Women's World Cup in Brazil, while Taiwan will compete with the other losing quarter-finalists for two more places in play-offs on the Gold Coast next week.