Angelique Kerber might yet celebrate her return to No. 1 with a BNP Paribas Open title after battling past Pauline Parmentier 7-5, 3-6, 7-5 to reach the fourth round on Monday.
The 31-year-old Russian, owner of two Grand Slam singles titles, enjoyed a resurgence in 2016, winning two titles and upsetting world number one Serena Williams in Miami as she returned to the top 10 in the world for the first time since 2010.
Venus Williams survived a scare against China's Shuai Peng, coming from behind to win 3-6 6-1 6-3, while Zvetlana Kuznetsova dismissed Johanna Konta's conqueror Caroline Garcia 6-1 6-4.
Second-seeded German Angelique Kerber notched one of her most convincing wins of the season at the BNP Paribas Open hard-court tennis tournament, cruising to a 6-2, 6-1 second-round victory over cmpatriot Andrea Petkovic in less than an hour.
"I know when she's down in the score, she's going for the shots".
After the Hungarian managed to consolidate the break with a tough hold of serve, Vesnina finally got onto the scoreboard in the second set as she had a nervy service hold, lessening the deficit to just two games.
Continuing to attack her shots with goal, the world No. 62 broke to start the second set then broke again at 15 extending the lead to 3-0.
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It was another turnaround for Williams, who prevailed 3-6 6-1 6-3, having fended off a match point against Jelena Jankovic earlier in the week. Some years it just hasn't quite happened for me.
"It was not my day", she said. "She's playing kind of this mix up a little bit of Spanish tennis, which I think is pretty good on these courts".
It was a tight first set was both Williams and Safarova were strong on serve, until an inspired Venus broke at in the ninth game of the set to go up 5-4 before serving it out to take the opening set 6-4.
"I was not thinking too much about her game", Kerber said. But obviously I don't want things to get close.
Former world No 1 Caroline Wozniacki also advanced, the 13th seeded Dane turning back qualifier Magda Linette of Poland 6-3, 6-0.
Kerber next faces Russian Elena Vesnina, a 6-4, 1-6, 6-4 victor over Hungarian Timea Babos.
The Czech will face reigning French Open champion Garbiñe Muguruza of Spain, a 7-6 (5) 1-6 6-0 victor over in-form Ukrainian Elina Svitolina.