Bertens, who had come into the tournament as an alternate after Naomi Osaka withdrew after her first match because of a shoulder injury, served for the opening set at 5-4 but was feeling unwell and quit after the tournament doctor came on court to examine her.
Due to Osaka pulling out due to injury, world number 10 Bertens will replace Osaka for the remaining matches and plays Barty in Red Group action on Tuesday.
Take down Kvitova and she'll top the Red Group and advance to Saturday's semi- finals.
Barty took the first set after breaking Kvitova in the fifth game, using her athleticism and movement around the court to put the Ukrainian under constant pressure. "I will just play and fight like always", she said.
Bencic made her pay and broke again in the 12th sport to grab the predominant recount and presently after registered her first victory over Bertens in an abbreviated fourth matchup between the pair.
Belinda Bencic claimed the second semi-final spot from Barty's group when an ailing Bertens called it quits while trailing the Swiss 7-5 6-1 in Thursday night's second match in Shenzhen.
Bertens came close to beating Barty in the Beijing semifinals this month, losing in a third-set tiebreaker.
'A little bit for them to give back to them when I'm back home in Australia at the end of the year. "(I felt) a little bit dizzy".
U.S. troops killed Baghdadi "replacement"
President Donald Trump announced Sunday U.S. commandos killed al-Baghdadi as he was hiding in northwestern Syria. A U.S. official told CNN that "the President was referring to ISIS spokesperson Abu Hasan al-Muhajir".
The organizer quoted Osaka as saying she is disappointed to have to withdraw from the event.
It kept her tournament hopes alive after she had lost her opening match to Barty.
Australian tennis superstar Ashleigh Barty is set to play against Petra Kvitova at the WTA Finals in China.
The world No 1 surged into a 4-0 lead in the second set and saved all four break points that she faced before securing her victory.
"Playing against Petra is probably one of my favourite things to do if I'm being honest".
"It's just incredible. The year she's had anyone would dream of having once in their career", Stosur told AAP.
Last year, she reached the semifinals in her WTA Finals debut. Even though it ended prematurely, Osaka was pleased with her back end to the season after a tough stretch where she suffered a stunning first-round exit at Wimbledon followed by a lacklustre US Open title defence.