Brisbane - Third-seeded Angelique Kerber secured the first spot in the quarter-finals of the Brisbane International with a 6-3, 7-5 win over Daria Gavrilova on Tuesday.
Varvara Lepchenko also advanced with a 6-4, 6-4 win over fellow American Madison Keys, who had ousted Australian Open finalist Dominika Cibulkova in the first round.
In a men's first-round upset, Lukasz Kubot of Poland beat fifth-seeded Kevin Anderson of South Africa 7-6 (3), 6-4.
At the ASB Classic in Auckland, New Zealand, Venus Williams made short work of her first match of the new year by sweeping past Slovakia's Jana Cepelova 6-4, 6-0 in 52 minutes.
Williams, seeded third behind Caroline Wozniacki and Sara Errani, appeared fit and served 10 aces.
The seven-time major winner reached the final of the Auckland hard-court tournament last year.
"It was very nice," Williams said. "I was welcomed when I came on the court and I felt like I left off right from last year. I felt comfortable right away."
Top-seeded Wozniacki had to work hard to subdue qualifier Julia Glushko of Israel 6-3, 6-2.
Urzula Radwanska beat former French Open champion Francesca Schiavone 6-4, 7-5 and another qualifier, Lucie Hradecka of the Czech Republic, toppled fifth-seeded Svetlana Kuznetsova 3-6, 7-6 (6), 6-4.
At the Hopman Cup in Perth, the Czech Republic beat Italy 3-0, with Lucie Safarova beating Flavia Pennetta 7-5, 6-3 and Adam Pavlasek scoring an upset win over Fabio Fognini in the men's singles. Fognini later withdrew before the mixed doubles.
Americans Serena Williams and John Isner were playing Canada's Eugenie Bouchard and Vasek Pospisil in a night match in Group A.