She then saw off world number two Angelique Kerber to reach the last eight but was slapped down by Russian Kuznetsova, who only ceded one break point in the entire match, which she saved.
The eighth seed then took Bouchard apart in the second set, breaking her four times before serving out the match.
Kuznetsova will face Kristina Mladenovic of France in the last four on Friday, with Anastasija Sevastova of Latvia meeting Romanian third seed Simona Halep in the other semi-final.
(Reporting by Richard Martin; Editing by Ken Ferris)
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