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.
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.