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Karolina Pliskova missed the cut despite her comeback victory over Barbora Krejcikova.
Osaka, 23, slipped from seventh to 12th position, ending her streak of 140 consecutive weeks in the top 10.
The Spaniard, a former world No.1, was down a set and a break but fought back strongly to beat Jabeur 3-6, 6-3, 6-0 to claim her second title of the year and ninth overall.
The field still boasts world No. 1 and reigning Wimbledon champion Ash Barty, four-time Grand Slam winner Naomi Osaka and reigning French Open champion Barbora Krejcikova.
Three-time Grand Slam champion Osaka will meet Jennifer Brady in the title match.
Osaka crushed Hsieh Su-wei 6-2, 6-2.
Osaka battled back from the brink to reach the quarterfinals.
The 22-year-old Kenin, who followed her Grand Slam breakthrough at Melbourne Park last year with a run to the final at the French Open, sprayed 22 unforced errors in the 64-minute contest against the experienced Estonian.
Badosa lost to Russian qualifier Liudmila Samsonova in three sets.
Iga Swiatek, who became the first Polish player to win a Grand Slam singles title when she beat Kenin in the French Open final, was named the WTA's Most Improved Player of the Year.