In front of 5238 fans on Saturday, China hit the lead in the fourth minute of extra-time through Shao Ziqin, before the deal was sealed in the 118th minute via an unlucky own goal to Chen Ying-hui.
The reward is a semi-final showdown against tournament hosts Australia at the 60,000-seat Optus Stadium on Tuesday night.
Australia secured their spot in the final four with a nervy 2-1 win over North Korea on Friday night.
"We probably created enough to win the game in 90. We didn't," China's Australian coach Ante Milicic said.Â
"And then I think it's normal with a game that's got so much on the line, we looked a little bit anxious.
"But in the end, I felt that we were fairly well in control. We won the game, qualified for the World Cup, and we moved into the semi-final. So I'm just delighted for the players."
World No.40 Taiwan must now head to the Gold Coast to fight for World Cup qualification against the other three Asian Cup quarter-final losers.
"I told them you don't need to be sad, you don't need to cry," Taiwan coach Prasobchoke Chokemor said.
"You can be proud. They put everything into it and showed a strong heart."
World No.17 China had a goal rubbed out in the 39th minute but still almost sealed the win without the need for extra-time when Yao Wei fired off a shot in the seventh minute of stoppage time - only for it to hit the upright.
Shao broke the deadlock early in extra-time with a curling strike from just inside the box, but Wurigumula had a penalty saved by Taiwan goalkeeper Chang Chi-Lan in the second period, keeping China on edge.
China made it 2-0 in the dying minutes of extra-time when a cross cannoned into Taiwan defender Chen Ying-Hui and in for a goal.
The match was played amidst a delicate political environment given China views self-ruled Taiwan as a breakaway province that will eventually be under Beijing's control.
There didn't appear to be a repeat of the controversy in Sydney, when former Taiwan coach Chen Kuei-jen was ejected from the stadium during the 3-1 win over India for leading a "Go Taiwan" chant.
Taiwan compete under the name Chinese Taipei in international sporting events.
China had 71.7 per cent possession in the first half of Saturday's match but it only translated to five shots - and just one on target - due to Taiwan's water-tight defence.
The one time China truly broke through was in the 39th minute when Zhang Xin's inch-perfect cross was headed in by Wang Shuang.
But China's celebrations were short lived, with the VAR revealing Wang had committed a handball in the lead-up play while attempting to chest down the ball.
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