Sania and her American partner Bethanie-Mattek Sands shocked second seeds Martina Hingis and Flavia Penneta, winning 6-3, 6-3 in the quarter-finals of Apia International. Rohan Bopanna and Daniel Nestor beat the Italian pair of Simone Bolelli and Fabio Fognini.
On a largely disappointing day for Indian tennis players, Leander Paes, Rohan Bopanna and Sania Mirza lost their respective doubles matches in the second round of the Australian Open, leaving the country's challenge restricted to the mixed doubles competition.
Third seed Rafael Nadal battled through mid-match cramps for more than an hour before he lurched into the third round of the Australian Open with a 6-2, 3-6, 6-7(2), 6-3, 7-5 victory over American qualifier Tim Smyzcek.
Defending champion Novak Djokovic moved confidently into the second round of Wimbledon with a 6-4, 6-4, 6-4 win over German Philipp Kohlschreiber on Monday.
Summary of sports events and persons who made news on Sunday
Wozniacki battles past Kerber into Eastbourne final
A late end to last season that included a successful Davis Cup final and matches in India had no impact on Roger Federer's surprise third round loss to Andreas Seppi at the Australian Open on Friday, the second seed said.
Serena Williams shook off the rust and a feisty challenge from Serbia's Ana Ivanovic to open the defence of her WTA Finals title with a 6-4, 6-4 victory in the opening match of the elite eight-player tournament on Monday.
Top seed Serena Williams made short work of Kazakhstan's Zarina Diyas in the third round of the BNP Paribas Open.
Two-time Grand Slam winner Victoria Azarenka crashed out of the French Open in the first round losing 5-7, 5-7 to Katerina Siniakova on Monday, playing only her fifth tournament of the year after a legal battle over the custody of her son.
A round-up of results from Davis Cup matches played on Saturday and Sunday
Roger Federer guided Switzerland to victory in their Davis Cup World Group playoff tie against the Netherlands with an easy 6-3, 6-2, 6-4 victory over Thiemo de Bakker on Sunday.