Thiem broke the 32-year-old Murray in the first game of the match, but the British player made things more difficult in the second set, testing his younger opponent's nerve in finishing out the match.
Also, Karen Khachanov of Russia beat Italy's Fabio Fognini 3-6, 6-3, 6-1, Alexander Zverev downed Sam Querrey, 7 (7)-6 (3), 6-2, and Stefanos Tsitsipas of Greece beat American John Isner 7-6 (3), 6-3.
Top-seeded Ash Barty reached the semifinals in the women's draw by beating Petra Kvitova 4-6, 6-4, 6-3. "From my opinion, that was one of the highest quality matches I played all year," said Barty, the French Open champion. "Petra always has a way of bringing out the best in me, she really does."
Barty converted three of her six break points while Kvitova, a two-time Wimbledon champion, was two for seven. In Saturday's semifinals, Barty will face eighth-seeded Kiki Bertens, who defeated Elina Svitolina 7-6 (6), 6-2.
"I think this week I played some better tennis again," said Bertens, who amassed 36 winners to Svitolina's 16. "I think then with some pressure and playing better all the time, it's good for me. It says for myself that I was growing a lot over the last few years."
Also, defending champion Caroline Wozniacki beat Daria Kasatkina 6-3, 7-6 (5) and will next face Naomi Osaka, the two-time Grand Slam champion from Japan who served 10 aces to end U.S. Open champion Bianca Andreescu's winning streak at 17 with a 5-7, 6-3, 6-4 victory.
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