Defeat for Halep means that Karolina Pliskova, at number seven, is the only women's top 10 seed to reach the fourth round.
Hsieh Su-Wei, who reached a career singles high ranking of 23 in 2013, welcomed the shake-up at the top of the sport.
Five-time champ Venus Williams became the latest star to crash out in a 6-2, 6-7 (5/7), 8-6 defeat against Kiki Bertens.
Replays showed the ball landed inside the sideline but umpire Marta Mrozinska refused to accept Pliskova's arguments to overturn the call.
Former world number one Karolina Pliskova held on to sixth place in the world rankings after her victory in the Stuttgart Grand Prix tournament.
There were no changes in this week's top 10, as Denmark's Wozniacki held the third position, followed by Czech Karolina Pliskova.
Pliskova launched her bid for a season-ending triumph at the WTA Finals with a convincing 6-2, 6-2 victory over Venus.
Romanian tennis player Simona Halep continued to lead the Women's Tennis Association rankings released.
World number two Simona Halep was booted out of the Wuhan Open 6-2, 6-1 by Russia's Daria Kasatkina on Tuesday.
Pliskova ill now face crowd favourite, Wang Qiang, the first ever Chinese player to reach the third round at Wuhan.
Rafael Nadal, Karolina Pliskova matches postponed by rain at Cincinnati Masters; Simona Halep advances
Pliskova led qualifier Camila Giorgi 3-0 when play was suspended while Nadal and Albert Ramos-Vinolas never started their third-round match.
Wozniacki posted her first career win over a number-one player in seven tries as she blasted eight aces in the two-hour.
Karolina Pliskova has become the new world number one, despite tumbling out of Wimbledon in the second round.
German Angelique Kerber remained at the top of the WTA world singles rankings released on Monday.