INDIAN WELLS, Calif. -- Svetlana Kuznetsova took another step forward in her comeback from a right knee injury.

Kuznetsova beat Andrea Hlavackova of the Czech Republic, 6-3, 6-1, in Wednesday's opening round of the BNP Paribas Open tennis tournament at the Indian Wells Tennis Garden.

Kuznetsova, twice a Grand Slam champion and two times a runner-up in this $10 million event, did not play following Wimbledon last season due to the injury and the former world No. 2 was ranked No. 85 on January 6. She is No. 46 now thanks in large part to quarterfinal showings at Sydney, Australia, and in the Australian Open and can continue her climb with a win over No. 18 Jelena Jankovic in the second round.

"I haven't played her for years and it's going to be a very interesting match," said Kuznetsova, a Russian who is living in Dubai. "I remember that her down-the-line backhand was quite good and normally her movement was good, but I haven't seen her play for a while, so we'll see how it goes.

"I'm happy to be back on the court, this is the main thing. Every day I just try the best I can and things are coming along pretty well. I feel really balanced within myself, which is important. I actually have my dog here in Indian Wells, which is great! I'm a happy person, I do my favorite job and we're here in this nice place with a lovely view and great weather. I think it's everything we need!"

In contrast to Kuznetsova, opening day wasn't a good day for the Americans. Mallory Burdette, a 22-year-old qualifier from Macon, Ga., was the only one of the quartet in action early Wednesday to advance to the second round, and she did it by beating another American, 38-year-old Jill Craybas, 6-3, 6-1.

Vania King, 24, started well by winning a first-set tiebreaker from Silvia Soler-Espinosa of Spain, but the Spanish Olympian rolled through the next two sets for a 6-7 (7), 6-2, 6-1 win. Lauren Davis, a 19-year-old Floridian, was a 6-2, 6-0 loser to 21-year-old Simona Halep of Romania.

Americans Christina McHale, Grace Min and Maria Sanchez played later in the day with McHale, at No. 48, meeting No. 50 Tsvetana Pironkova of Bulgaria in one of the potentially closest matches.

Ksenia Pervak of Kazakhstan, No. 93, sprang the first upset of the tournament by toppling Nol. 42 Jie Zheng of China, 6-1, 6-2. Johanna Larson of Sweden, Chanelle Scheepers of South Africa and Olga Govortsova of Belarus were other first day winners.

The women's first round continues and the men's first round gets under way Thursday. All 32 seeded players in both the men's and women's fields have opening-round byes.

Victoria Azarenka and Novak Djokovic are the reigning champions. Djokovic, a perfect 12-0 this year, is seeking his third Indian Wells title.