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Karen Khachanov defeated Czech teenager Jakub Mensik to win his sixth career title at the Qatar ExxonMobil Open in Doha.
While Shang fell short in his bid to become the first Chinese man to reach the fourth round of a Grand Slam in the Open era, the country will have a women's singles player in the second week as 12th seed Zheng.
The 22-time Grand Slam champion overpowered Kubler in 83 minutes to book his place in the last eight.
Karolina Muchova overwhelmed Sorana Cirstea and will meet American Coco Gauff in the semifinals.
Djokovic improved his record against American opposition at the US Open to a perfect 12-0.
The 2017 Roland Garros champion next faces American sixth seed Coco Gauff, who beat wildcard Caroline Wozniacki in three sets earlier in the day.
The Czech is only the third player ranked outside the top-40 to reach the final at Roland Garros.
Azarenka rolled back the years as the two-time champion crushed third seed Jessica Pegula 6-4, 6-1.
The Indians progressed after Jelena Ostapenko and David Vega Hernandez pulled out of the mixed doubled quarterfinals.
The Indian pair defeated Japan's Makoto Ninomiya and Uruguay's Ariel Behar 6-4, 7-6(11-9).