Shao Ziqin brilliantly fired into the right corner in the 94th minute before earning a penalty in the second-half of added time.
Substitute Wurigumula missed the spot kick but China sealed victory at Perth Rectangular Stadium through an own goal from Chen Ying-hui.
It kept China's bid for a record-extending 10th title on track, with victory also ensuring their direct qualification for the 2027 World Cup in Brazil.
They will face the Matildas on Tuesday at the 60,000-seat Perth Stadium after the hosts edged North Korea 2-1 in the last eight.
China will be without star midfielder Wang Shuang, who was handed a yellow card for the second straight match.
"Of course, she's a loss. There is going to be an opportunity for someone else," China head coach Ante Milicic said.
"These girls are so resilient. I'll back my girls against any opponent."
Taiwan now move to a play-off against North Korea with an automatic World Cup spot on the line.
"They put everything they have on the pitch and showed how strong their heart is," Taiwan head coach Prasobchoke Chokemor said.
"We are still on the way to chase our dream of the World Cup."
The quarter-final had political undertones given China's claim to the self-ruled island of Taiwan, who compete under the name "Chinese Taipei" in international sports events.
It is part of a political compromise with China that allows them to take part in major competitions without presenting itself as a sovereign nation.
The crowd of 5,238 was relatively split between the fan bases although the Taiwanese contingent were more vocal.
There were some flag-waving Chinese fans wearing shirts with the words "China is my faith" written on the back.
Like China, Taiwan has enjoyed strong support at the tournament but controversy erupted in the stands during their last game in Sydney.
Former Taiwan coach Chen Kuei-jen was ejected from the stadium for leading a "Taiwan Jiayu", or "Go Taiwan", chant.
There did not appear to be a repeat on Saturday.
Taiwan are known for their dogged defence but unfurled attacking flair in the early exchanges.
China gained control in the midfield and dominated possession and appeared to capitalise just before the interval when Wang headed home, triggering jubilation from the Chinese fans.
But their celebrations were cut short when the goal was overturned due to a handball by Wang earlier in the chain.
China put the foot on the gas after the break, but Taiwan threatened on the counter-attack.
In the last stages of regulation time, substitute Yao Wei's bullet hit the crossbar as the match went into extra-time where Shao stepped up.