Earlier in the day, world number three Aryna Sabalenka suffered a shock loss in her first match, falling to Italian Jasmine Paolini 2-6 6-3 6-3 in the second round.
The hard-hitting Belarusian's serve was broken four times and she committed 10 double faults on a hot day in the Southern California desert.
Diminutive world number 46 Paolini said she was as surprised as anyone to come away with her first win over a top 10 opponent.
“I'm so happy. I didn't expect this moment,” she said.
“I'm just happy to be here in the third round. I think I played an amazing match. The crowd was amazing. I enjoyed it very much.”
Sabalenka was a favourite to win the event after world number one Ash Barty and world number two Barbora Krejcikova withdrew ahead of the start of the WTA 1000 tournament.
Sabalenka follows Karolina Pliskova and Garbine Muguruza out the door after both top 10 players lost on Friday.
Paula Badosa also kicked off her title defence with a 6-2 7-6(4) win over Tereza Martincova.
The Spaniard had never taken a set off the Czech in their three previous meetings and let out an emphatic scream and pumped her fists after she executed a perfect backhand volley winner on match point.
“I think the difference was I played against her one-and-a-half years ago and I've improved a lot in so many ways,” Badosa said.
“Mentally, but physically as well because I think it was a very physical match. I could see how much I improved today.”
Wearing the colours of the Ukrainian flag, Russian-born qualifier Australian Daria Saville upset ninth-seeded Ons Jabeur 7-5 6-7(0) 6-4 in their second round clash.
The Tunisian Jabeur reached the semifinals of the tournament last year but Saville's relentless return game and defence ultimately won the day.
Petra Kvitova needed every ounce of strength she had to battle past Aliaksandra Sasnovich 6-7(4) 6-4 6-4.
The two-time Wimbledon champion took a knee on the court and bowed her head after firing a forehand down the line to end the gruelling contest. She will next face sixth-seeded Greek Maria Sakkari, who was a straight sets winner over Katerina Siniakova.
American Amanda Anisimova retired before the third set of her match against Canadian teenager Leylah Fernandez with an apparent illness.
In other second round action, American Shelby Rogers was all smiles after taking down Latvian 10th seed Jelena Ostapenko and fourth-seeded Anett Kontaveit needed just over an hour to cruise past Slovakia's Kristina Kucova 6-4, 6-1.