The British number two is through to her first WTA Tour semi-final in more than a year after surviving a topsy-turvy contest to prevail 7-5 6-7 (4) 7-6 (6) in three hours and two minutes.
This has been by far the best week of a generally miserable season for Watson and the victory ensures she will return to the top 100 next week.
Watson's second-round win over second seed Wang Qiang was her most impressive for more than two years and in Linette she faced a player who has had a fine season.
In a match complete with twists and turns, Heather was in phenomenal form to clinch a 7-5, 6-7(4), 7-6(6) victory over eighth seed Linette 👏👏👏 pic.twitter.com/BXg6nx3KIr
— LTA (@the_LTA) October 11, 2019
The Pole won her first WTA title in New York in August and reached the final in Seoul last month, while in Beijing last week she lost just three games to Watson in a qualifying match.
Having won the last five games of the first set, Watson had a match point when serving at 5-3 in the second but Linette saved it and levelled the contest.
The eighth seed then had four chances to win the match on Watson's serve at 4-5 in the decider but each time the 27-year-old stood firm and she took her third match point in the deciding tie-break.
Speaking in an on-court interview broadcast by BT Sport, Watson said: "I'm so full of emotions right now. That match was so up and down from both of us. I only played Magda last week and she killed me so I knew I really had to step it up."