Wild-card entrant Eugenie Bouchard of Canada, who struggled recently, and defending champion Svetlana Kuznetsova advanced with first-round victories on Sunday at the Apia International Sydney event in Sydney, Australia.
This tournament is a tune-up event for the Australian Open, which begins Jan. 16.
The 22-year-old Bouchard, who in 2014 reached the finals at Wimbledon and the semifinals of both the Australian Open and French Open, lost in the first round in Brisbane in her first warmup event this season, but she beat Shuai Zhang of China 7-6 (1), 6-2 in her opener at Sydney.
Bouchard, who was ranked as high as No. 7 in 2014 but is currently at No. 46, broke the serve of the 23rd-ranked Zhang three times on her way to victory. It was just her second victory since August, and she responded to her critics after the match.
"First and foremost I play tennis for myself," Bouchard said. "I want to prove to myself and to everyone that I can do it and I can be successful. I'm on that path. There's a long way to go, but I hope I can do that."
No. 5 seed Kuznetsova of Russia advanced to the second round with a 6-1, 6-4 win over Irina-Camelia Begu.
"I started the year quite good with the feeling on court," Kuznetsova said. "Sometimes the results don't go with how you're feeling, but I feel very good at the start of the year."
Kuznetsova rolled to an early advantage, winning 10 of the first 12 games. Begu, of Romania, rallied to tie the second set at 4-4.
Kuznetsova then closed out the match by winning the next two games.
"I'm not thinking about defending my title," she said. "The trophy is at home and nobody can take it away from me. This is another year and another opportunity to play. I always feel like I need a lot of matches at the start of the year. I remember going to Auckland and not winning a single match. Then I came here and it gave me matches, confidence."
Yulia Putintseva of Kazakhstan advanced when Belinda Bencic of Switzerland retired with a toe injury when Putinseva was leading 6-4, 2-3. Putintseva next plays the winner of the match between Denmark's Caroline Wozniacki and Puerto Rico's Monica Puig.
"It was very good quality for me, that first set," Putintseva said. "Belinda was playing well, I was playing well and we had a lot of good rallies. But I'm really happy to get my first win of 2017 so far. Looking forward to my next match."
Daria Kasatkina of Russia defeated Temea Babos of Hungary 3-6, 6-4, 6-2.
Several players withdrew from the Sydney event, but No. 1 Angelique Kerber remains in the draw.