Bertens continued her sturdy type after making the finals in Zhuhai final week and the semi-finals of the China Open earlier within the month, when she misplaced a three-set thriller to Barty.
Bencic's victory means all four players can still finish in the top two in Red Group and progress to the last four from the round-robin stage.
Kvitova would nearly have the chance to break back after Barty double-faulted at deuce serving at 5-2, but the Australian kept it clutch and managed to stave off her fourth break point of the opener.
"Actually I did this in the finals of Beijing", she said at a news conference.
Kvitova rued her inconsistency in the first and third sets. The Australian, who still is very much alive in the WTA Finals has surpassed the $10 Mn prize money in 2019, taking it to $10.93 million with a possibility to earn more.
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In the later match, Bencic fought back from a second set spiral to beat Kvitova 6-3, 1-6, 6-4 in one hour and 47 minutes.
Osaka said she will have a detailed examination in Japan, and aims to make a return at the Brisbane International in January. Neither player has looked at their best in this tournament but I with less pressure, I feel Kvitova will be able to fully express her ability. It's just a little bit painful.
But even if she loses and misses the semi-finals, the 23-year-old will leave China $890,000 better off.
World No. 4 Andreescu had lost her opener against Simona Halep in a three-set thriller on her WTA Finals debut.
Following a title on her favorite surface of grass in Birmingham, England in June, Barty became the first Australian woman to top the rankings since her mentor, Evonne Goolagong Cawley, in 1976. I could play a little bit more aggressive, come to the net.
"I'm disappointed to have to withdraw from the Finals", Osaka was quoted as saying on the WTA website.
"It's just incredible. The year she's had anyone would dream of having once in their career", Stosur told AAP. "I just want to try to duplicate that".