Elina Svitolina hit the ground running in Singapore, beating Petra Kvitova for the first time in four years.
Olga Danilovic became the first player born in the 21st century to win a WTA title in Moscow at Anastasia Potapova's expense.
Misaki Doi and Timea Babos reached the OEC Taipei WTA Challenger final at the expense of Evgeniya Rodina and Kirsten Flipkens.
A 6-0 6-3 victory over Flavia Pennetta saw Simona Halep get her WTA Finals campaign off to a promising start.
There were no surprises at the Hong Kong Open on Thursday as the four seeds in action all made it through to the quarter-finals.
World number four Garbine Muguruza will not compete at this week's Hong Kong Open due to an ankle injury.
Reigning French Open champion Simona Halep says tennis is more open now and anyone could win a Grand Slam.