Kvitova has now lost both her matches and needs results to go her way in the White Group to stay afloat in the season-finale.
The 28-year-old Caroline Wozniacki had won the China Open in 2010.
Caroline Wozniacki and Angelique Kerber suffered shock defeats at the hands of less fancied opponents.
World number two Caroline Wozniacki and Wimbledon champion Angelique Kerber eased through their opening matches at the Wuhan Open in China on Tuesday.
Romania's Simona Halep continued to lead Women's Tennis Association (WTA) rankings released on Monday, ahead of Denmark's Caroline Wozniacki.
Hard work and peak fitness are the major concerns for world number two Caroline Wozniacki as she starts her first run to the US Open as a Grand Slam champion.
Caroline Wozniacki suffered fresh Wimbledon woe as the world number two suffered a shock 6-4, 1-6, 7-5 defeat against Ekaterina Makarova in the second round on Wednesday.
Novak Djokovic cruised through to the French Open second round in straight sets.
Simona Halep needed to reach at least the last eight and go further than world number two Caroline Wozniacki to retain the top-ranking going into the French Open.
Caroline Wozniacki says it would be "impossible" for her to follow Serena Williams' lead and return to tennis after giving birth.
Kasatkina recorded her second straight win over Wozniacki, having also beaten the reigning Australian Open champ at the St. Petersburg tournament last month.
An irritated world number one Caroline Wozniacki progressed to the Qatar Open quarter-finals on Thursday in a feisty match where she complained and apparently mocked her opponent Monica Niculescu's grunting.
Rafael Nadal is leading the latest ATP Rankings with 9,760 points while Caroline Wozniacki leads the Women's list with 7,965 points.
The Dane, who will become the new world number one, burst into tears as she secured the championship.
In a see-sawing contest, Halep sprinted into a 6-3, 3-1 lead before the 2016 Melbourne Park winner, seeded 21, fought back.
Second seed Caroline Wozniacki withstood a fightback from Spain's unseeded Carla Suarez Navarro to stutter into the semi-finals of the Australian Open.
The assured Dane, a semi-finalist in 2011 who has never quite lived up to the hype in the majors, annihilated 19th-seeded Magdalena Rybarikova 6-3, 6-0 on Rod Laver Arena in her most impressive performance to date.
Rafael Nadal stormed into the round of 16 at the Australian Open Friday with a vintage performance as Grigor Dimitrov and Caroline Wozniacki kept their Grand Slam hopes alive on a hot draining day.
