Saville lost 0-6 6-7 (6-8) on Wednesday ending Australian interest in the WTA's first competition in China since before COVID-19.
Linette will meet fifth-seeded Rebekah Masarova in the quarterfinals. The Spaniard beat Viktorija Golubic 6-1 3-6 7-6 (9-7).
Third-seeded Tatjana Maria and fourth-seeded Lucia Bonzetti also progressed to the quarterfinals. Maria beat Bai Zhuoxuan 6-1 6-2 and Bonzetti defeated Moyuka Uchijima 6-3 6-3.
Bonzetti will next play seventh-seeded Greet Minnen who outlasted British qualifier Harriet Dart to win 7-6 (9-7) 6-7 (5-7) 6-4 after three hours and 14 minutes.
At the Chengdu Open eighth-seeded world No.50 Aleksandar Vukic was upset in the opening match on centre court by Taro Daniel, 45 places his inferior, 4-6, 6-4, 6-2. Daniel may now meet another Australian, Christopher O'Connell, if the latter gets past qualifier Alibek Kachmazov.
Philip Sekulic came through qualifying while Jordan Thompson and sixth-seeded Max Purcell are also in the draw, and face each other in the last 32.
Elsewhere Roman Safiullin defeated Brandon Nakishima 6-4, 6-4 and Corentin Moutet defeated Chinese wild-card Mu Tao 6-2, 6-2.
In the Zhuhai Championships Alex Bolt, Luke Saville, Marc Polmans and Dane Sweeny have all come through qualifying with the latter pair drawn against each other in the tournament proper. Rinky Hijikata is also in the main draw having qualified by ranking.
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