Mladenovic upset Osaka in straight sets two weeks ago at the Dubai tournament.
It was a good day for veteran Venus Williams, who surged past Petra Kvitova.
"The tournament in Australia was unbelievable considering all these things, the only regret is that I could not compete at my best in the final but I found a great Djokovic", Nadal told ESPN this week.
Two-time Grand Slam victor Osaka sealed her tenth victory of the season.
The match was Osaka's first as the world's top player and as the reigning Australian Open champion - and she was contesting it coachless after parting ways with Sascha Bajin shortly after her Melbourne triumph.
Naomi Osaka and Danielle Collins are going to face each other in the 3rd round in Indian Wells.
American Sampras, a 14-time Grand Slam victor, was in the stands as the Serb beat Fratangelo 7-6 (7-5) 6-2.
"I've never been a defending champion before, that's new and I was really nervous", said Osaka, who booked a third-round meeting with American Danielle Collins, who was a 6-4, 6-1 victor over Kirsten Flipkens.
Alexandrova put her hands over her face in disbelief when Wozniacki was unable to return her serve on match point.
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Another resident, Rubina Bibi, 32, said she wants peace "so that we can live without leaving our own villages" in Kashmir. The high tensions last week displaced hundreds of villagers on both sides.
She booked a third-round clash with fellow American Christina McHale, a 6-4, 3-6, 6-4 victor over 30th-seeded Russian Anastasia Pavlyuchenkova.
"Well, I mean, I really used to just dislike night matches because you're, like, the last one there, and honestly I sleep kind of early", Osaka addressed the press of the Indian Wells 2019.
Karolina Pliskova booked her place in the third round after a hard-fought win over qualifier Misaki Doi.
The Czech appeared to have taken control of the stadium court slugfest when she broke Williams for a 4-3 lead in the third.
Eighth-seeded German Angelique Kerber eased into the third round with a 6-0, 6-2 victory over Kazakhstan's Yulia Putintseva.
Next up for Barthel is a meeting with countrywoman Julia Gorges, who beat Estonian Kaia Kanepi 6-3 2-6 6-3 behind seven aces in an evening match.
Coming off an impressive title win in Acapulco, Kyrgios went down to German veteran Philipp Kohlschreiber 6-4 6-4.
The latter had won the Mexican Open last week. "I served really well today, so that was obviously a big key".
India's Prajnesh Gunneswaran continued his supreme form.
He is set to take on Ivo Karlovic in the third round.