Defeated 2-0 by Japan in their opening game, Su Yu-Hsuan followed in a deft chip from Saki Matsunaga and headed home after it hit the crossbar in the 25th to give Taiwan the lead.
It was a margin they defended doggedly for the remainder of the contest at Perth Oval on Saturday.
The win moves Taiwan, who made the quarter-finals of the 2022 iteration after a 23-year absence from the knockout stages, up to second in Group C and, with a game against 67th-ranked India remaining, well-placed to progress through to the last eight.
After requiring a 94th-minute goal to defeat India in their opening fixture, Vietnam will now need to secure a result against tournament favourites Japan to ensure their progression to the knockout stages, or, failing that, avoid a defeat heavy enough to knock them out of contention to be one of the two best third-placed group finishers.
Mai Duc Chung's side threw themselves forward with desperation across the second half in search of an equaliser, but, under a stifling afternoon sun in Western Australia, were unable to break down their opponents' rearguard action.
The Golden Star Women Warriors, one of the preeminent powers in Southeast Asian women's football, thought they'd won a penalty in the 67th minute when Nguyen Thị Bich Thuy volleyed an attempt goalward and saw it clatter off the arm of Taiwan's Su Sin-Yun.
But referee Lara Lee was unmoved by their appeals, and VAR review determined that the defender's arm was in a natural position.
Kept in the game by strong saves from Tran Thi Kim Thanh that denied Wu Kai-Ching and Yu-Hsuan, Vietnam's desperate search for an equaliser created a series of chances, but wasteful finishing sunk their efforts, with just one of their eight shots sent on target.
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