Williams is playing in her first tournament since she withdrew from the U.S. Open in August after being diagnosed with a fatigue-causing autoimmune disease.
She showed plenty of staying power against the third-seeded Kvitova, taking charge in the final set. When Kvitova pushed a weary forehand wide on the final point after nearly 2½ hours, Williams trotted to the net with a grin and raised fist.
A former No. 1 and seven-time Grand Slam singles champion, Williams is ranked No. 134 and needed a wild card to enter the tournament, which she has won three times. She hopes to improve her ranking enough in the coming weeks to qualify for the London Olympics.
She showed plenty of staying power against the No. 3-seeded Kvitova, taking charge in the final set. When Kvitova pushed a weary forehand wide on the final point after nearly 2 ½ hours, Williams trotted to the net with a grin and raised fist.
Defending champion Victoria Azarenka won her 24th match in a row and first since arriving at Key Biscayne when she beat Michaella Krajicek, 6-3, 7-5.
The top-ranked Azarenka's streak began with her first match this year, and her start is the best since Martina Hingis went 37-0 in early 1997.
“I'm not really thinking about numbers, the streaks, whatever,” Azarenka said. “It's your job to count; mine is to play tennis.”
Azarenka won her first Grand Slam title in January at the Australian Open, where she beat Maria Sharapova to earn the No. 1 ranking. She also has won titles this year at Sydney, Doha, and—just a week ago—Indian Wells.
When asked to give a reason for the streak, Azarenka wavered.
“There is not really an answer,” she said. “There is one thing that I do, and it keeps happening for me: to win. There is really no magic.”
On the men's side, No. 10 seed John Isner overcame a slow start to beat Nikolay Davydenko 2-6, 6-3, 6-4. Davydenko retreated eight feet behind the baseline to better cope with the 6-foot-9 Isner's booming serves, but failed to break in the final two sets.
Williams took plenty of big swings against Kvitova, as though eager to hit winners and keep rallies short. She was 0 for 5 on break-point chances before she converted in the 10th game, taking the opening set when Kvitova netted a backhand.
A timid second serve gave Williams problems, but she repeatedly came up with clutch shots on break points, saving nine of 11.
Kvitova, who was slowed by a virus earlier this year, fell to 3-5 on North American hard courts since winning Wimbledon.
Alisa Kleybanova, playing in her first tournament since being diagnosed with Hodgkin's Lymphoma last May, lost to No. 22 Maria Kirilenko 7-6 (1), 6-3.
No. 15 Ana Ivanovic lost only six points on her first serve and beat American Vania King 6-4, 7-5. Ivanovic was playing for the first time since she retired with a left hip injury a week ago at the Indian Wells semifinals.
Two wild cards eliminated seeded women. Garbine Muguruza Blanco of Spain upset No. 9 Vera Zvonareva 6-4, 6-3, and Aleksandra Wozniak of Canada rallied past No. 28 Monica Niculescu 4-6, 6-3, 6-4.
Other seeded women eliminated included No. 11 Francesca Schiavone, No. 18 Angelique Kerber, No. 27 Lucie Safarova, No. 31 Kaia Kanepi and No. 32 Nadia Petrova.
No. 4 Andy Murray, the 2009 champion, beat Alejandro Falla 6-2, 6-3. Also advancing were No. 6 Jo-Wilfried Tsonga, No. 9 Janko Tipsarevic, No. 13 Gilles Simon, No. 16 Kei Nishikori and No. 18 Alexandr Dolgopolov.