Murray, bidding for his fifth tour title in China and the first there since the Beijing Open in 2016, edged a tight first set by breaking in the 12th game. The seventh-seeded Brit then overpowered his 23-year-old opponent in the second set to take the match in 1 hour and 42 minutes.
Giron, ranked No. 64, will next play Frenchman Arthur Rinderknech, who beat Tu Li 7-6 (5), 7-6 (6), while Thompson faces Dusan Lajovic. The Serbian needed three sets to overcome Belgian wild card Zizou Bergs 6-4, 1-6, 6-3.
At the Guangzhou Open, unseeded Yulia Putintseva from Kazakhstan beat third-seeded Tatjana Maria 6-4, 6-7 (6), 6-0 in a near 3-hour match to reach her first semifinal of a WTA 250 event since Istanbul in April 2022.
Greet Minnen defeated fourth-seeded Lucia Bronzetti of Italy 6-7 (8), 6-4, 6-1. The seventh-seeded Belgian will play either Wang Xiyu or Viktoria Hruncakova, who play later Thursday, in the semifinals.