Holland's Bertens, who arrived in Wuhan just hours before her opening match after winning the Korean Open last week, broke Swiss Bencic's serve five times and sealed victory with an ace.
World number 31 Dominika Cibulkova of Slovakia was a straightforward winner, defeating Romania's Monica Niculescu 6-4 6-3, while Polona Hercog of Slovenia lost 6-2 7-5 to China's Zhang Shuai.
Madison Keys of the United States beat qualifier Yafan Wang of China 6-3 6-3, but American wildcard Bernarda Pera lost 6-4 6-3 to another Chinese qualifier, Xiyu Wang.
There were also straight-sets wins for Australia's Ashleigh Barty, who beat Britain's Johanna Konta 7-5 6-4, and Spain's Garbine Muguruza, who defeated Alison van Uytvanck 6-4 6-0.
Donna Vekic of Croatia was beating Coco Vandeweghe 6-4 3-6 2-1 before the American retired just after two hours into the contest.
Aleksandra Krunic of Serbia beat Italy's Camila Giorgi 6-4 4-6 6-4 and Belarus' Aryna Sabalenka claimed a 7-6 (7/2) 2-6 6-2 win over Carla Suarez Navarro of Spain.
American qualifier Sofia Kenin also won, beating Chinese Taipei's Hsieh Su-wei 6-1 6-1.
Australia's Daria Gavrilova, China's Wang Qiang, Switzerland's Viktorija Golubic and Czech Republic's Barbora Strycova also progressed.
At the Tashkent Open in Uzbekistan, Canada's Eugine Bouchard was beaten 6-3 6-3 by Nao Hibino of Japan.
Fourth seed Stefanie Voegele of Switzerland suffered a 4-6 7-6 (7/3) 6-3 defeat to Russian qualifier Anastasia Potapova.
Fifth seed Tatjana Maria of Germany won 6-1 6-2 against Russia's Natalia Vikhlyantseva and eighth seed Dalila Jakupovic beat fellow Russian Anna Blinkova 6-4 5-7 6-4.
Sixth seed Anna Karolina Schmiedlova claimed a 6-3 6-0 victory over qualifier Dejana Radanovic.
There were also wins for France's Fiona Ferro, Maragerita Gasparyan of Russia and Fanny Stollar, a Hungarian qualifier.
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