The French-speaking Medvedev, cheered on by a partisan crowd, finished off a tired-looking Thiem 6-3 6-1 to end the Austrian's six-match winning streak in under an hour.
The Russian faces sixth-seeded compatriot Karen Khachanov or German third seed Alexander Zverev in the last four.
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So dominant was the tall Medvedev that he took the first five games of the second set winning 16 of the first 17 points.
He missed a chance to close out the match on Thiem's serve at 5-0 before sealing victory with an ace, his sixth of the day,
The Russian broke Thiem at the start of the match and never trailed, claiming the final two games of the opener as the Austrian's unforced errors piled up.
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