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.
Caroline Wozniacki saved two match points to scrape through to the third round of the Australian Open.
Organisers of the Sydney tournament, a warm-up for the first Grand Slam of the year, said Julia Goerges had pulled out with a right knee injury.
Wozniacki found herself a set down in her quarter-final against 19-year-old American Sofia Kenin but she regrouped to beat Kenin 4-6, 6-2, 6-4.
Caroline Wozniacki took to Twitter to announce her engagement to NBA star beau David Lee on Saturday morning.
Caroline Wozniacki had won just one set from seven harrowing defeats to Venus Williams.
Wozniacki was furious that her second round match was played on an outside court while five-time major winner Sharapova was playing all of hers in Arthur Ashe Stadium.
Five tennis players have a chance to grab the world No 1 ranking at this week's Cincinnati Open.