World number one Naomi Osaka launched her Indian Wells WTA title defense with a 6-3, 6-4 victory in a grudge match against Kristina Mladenovic on Saturday.

Osaka, whose second straight Grand Slam title at the Australian Open in January propelled her to the top of the rankings, was beaten by 65th-ranked Mladenovic in Dubai last month in her first match since she lifted the trophy in Melbourne.

Keen to avoid a repeat, Osaka marched through the opening set in 38 minutes, but she hit a speed bump as she was broken when serving for the match at 5-2 in the second.

After Mladenovic held serve to narrow the deficit to 5-4, the Japanese player faced another break point before wrapping up the match after one hour and 21 minutes.

She booked a third-round meeting with American Danielle Collins, a 6-4, 6-1 winner over Kirsten Flipkens.

Seven-time Grand Slam champion Venus Williams pulled off the upset of the day, rallying from a set and two breaks down to topple third-seeded Petra Kvitova 4-6, 7-5, 6-4.

"I just fought and tried my hardest," said Williams, currently ranked 36th in the world.

She booked a third-round clash with fellow American Christina McHale, a 6-4, 3-6, 6-4 winner over 30th-seeded Russian Anastasia Pavlyuchenkova.

There was disappointment, too, for 2011 winner Caroline Wozaniacki, who fell 7-5, 2-6, 7-5 to 59th-ranked Russian Ekaterina Alexandrova.

 Elsewhere on Saturday, fifth-seeded Karolina Pliskova shook off a slow start to defeat Japanese qualifier Misaki Doi 6-7 (4/7), 6-1, 6-1.

Pliskova next faces another qualifier, Belgian Ysaline Bonaventure, who defeated 28th-seeded Donna Vekic of Croatia 1-6, 7-6 (7/5), 6-4.

Eighth-seeded German Angelique Kerber eased into the third round with a 6-0, 6-2 victory over Kazakhstan's Yulia Putintseva.