Simona Halep survived a scare as she lost the first set against 19-year-old American Caroline Dolehide, the world number 165, but won 1-6 7-6 (7-3) 6-2.
World no 20 and French Open Champion Ostapenko, lost 6-3 6-3 to Croatia’s Petra Martic.
Sixteen year old American Amanda Anisimova, , caused an upset when she knocked out ninth seed Petra Kvitova 6-2 6-4.
“I’m still in shock,” said Anisimova, who is 149th in the world rankings. “She’s the best player I have ever played, and it was the biggest court I have ever played on.
“I was enjoying the moment, but at the same time, I was trying not to make myself nervous because of the huge crowd, and everything, and the big stage. “I have been working on that a lot, just not showing any emotions, just fighting the whole time. “I have been doing that really well these past two weeks.”
Anisimova won her first-ever WTA main-draw match at last week in Indian Wells in straight sets against Pauline Parmentier. Faced with a stiffer challenge in her next match against No. 23-ranked Anastasia Pavlyuchenkova, Anisimova didn’t blink, winning again in straights.
US Open champion Sloane Stephens beat Victoria Azarenka 6-1 7-5 who was playing her first tournament in eight months because of an ongoing custody battle over her son.
Novak Djokovic suffered a shock defeat by world number 109 Taro Daniel of Japan 7-6 (7-3) 4-6 6-1 in the second-round of the BNP Paribas Open at Indian Wells.
The game was the Serb’s first Tour match since withdrawing from the Australian Open in January through injury.
“For me it felt like first match I ever played on the tour,” said Djokovic. “Very weird. I mean, I just completely lost rhythm, everything.
“I just struggled also a little bit with the health the last couple of weeks. “I was grateful to be out on the court after surgery that quickly.
Obviously having only played a couple of matches in nine months, you’re still, in a way, battling inside of your mind whether you’re fit or not,” he added.
“And even though you don’t have pain, you’re still thinking about it, because it’s been something that I have been feeling and dragging for over two years.
World number one Roger Federer booked his place in the third round with a 6-3 7-6 (8-6) victory over Argentina’s Federico Delbonis. The match was carried over from Saturday after rain force play to end early with Federer one set up and the scores locked at 2-2 in the second.