Watson - Britain's number two after Johanna Konta - defended four match points to ultimately beat Linette 7-5 6-7 (4-7) 7-6 (8-6) in a three hours and two minutes epic.
Speaking after the match Watson said: "I'm so full of emotions right now - that match was so up and down from both of us."
Linette beat Watson in their first meeting which took place in Beijing at the end of September.
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However, Watson has looked to be on much better form during this tournament than across the rest of a disappointing season.
Currently ranked 125th in the world, the win will see Watson return to the top 100.
The 27-year-old will now play Veronika Kudermetova in the semi-final.
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