(REUTERS) - Serena Williams won her 750th career tennis match to stay on track for her ninth Miami Open title, when she beat Zarina Diyas of Kazakhstan 7-5, 6-3 in the third round in Florida on Saturday.

The world No. 1 improved her career record to 750-125, seventh on the all-time list and just three match wins behind Lindsay Davenport's 753. Martina Navratilova sits atop the all-time list with 1,442 wins.

The 34-year-old Williams will meet Russian Svetlana Kuznetsova in the fourth round. The 15th seed defeated France's Caroline Garcia 4-6, 6-2, 7-6 (8-6).

Unlike the last time they met, when Williams required 54 minutes and Diyas won just two games, the 22-year-old Kazakh gave the American some trouble in the heat and humidity of Miami.

Williams jumped out to a 4-0 lead in the second set, only to see Diyas rally and win three straight games. But the 21-time Grand Slam champion steadied to close out the match.

"I think she called her coach and they used a different strategy," Williams said in a courtside interview.

"I was able to figure it out after a little bit. She played well, especially to be ranked 97th. She has a bright future because she's so young. But I really wanted to close it out."

Williams and Kuznetsova were joined in the fourth round by Poland's Agnieszka Radwanska, Romanian Simona Halep, Swiss Timea Bacsinszky, Russian Ekaterina Makarova and wild card Heather Watson of Britain.

Makarova, the 30th seed, upset eighth seed Czech Petra Kvitova 6-4 6-4.