Vogele needed just over an hour to dispatch the fourth-seeded Stephens and push her overall record to 4-1 against the 2017 U.S. Open champion, who committed her 32nd unforced error on match point when she sent a forehand wide.
"Obviously playing someone who you haven't done that well against in the past is a little bit rough," Stephens told reporters after the match, which was played amid high winds on a sunny day in the Southern California desert.
"It was windy but it was windy for both of us. I just didn't play a great match today."
Under the lights on the stadium court, Williams smashed 39 winners to defeat Azarenka 7-5 6-3 in a rematch of the 2016 final, which the Belarusian won.
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"I truly love her, she's a really good friend," 23-times Grand Slam champion Williams said.
"She's a fellow mom and a former number one, just like me.
"It's hard to play someone you're so close with but it's also really invigorating and cool."
William will play Garbine Muguruza in the third round after the 20th-seeded Spaniard crushed American Lauren Davis 6-1 6-3 earlier on Friday.
Unseeded American Jennifer Brady defeated 19th-seeded Caroline Garcia 6-3 3-6 6-0 to book her place in the third round.
The 23-year-old Brady thumped five aces en route to her third victory over the Frenchwoman this year, setting up a meeting with 12th-seeded Ash Barty, who defeated Tatjana Maria 6-4 6-4.
Czech Marketa Vondrousova eased past error-prone Russian Daria Kasatkina 6-2 6-1 to book her place in the third round.
With the loss, 14th seed Kasatkina, a finalist at Indian Wells last year, is projected to fall out of the top 20 when rankings are next updated.
Second seed Simona Halep, Latvia's Jelena Ostapenko, Britain's Johanna Konta, Belgian Elise Mertens and 18-year-old Bianca Andreescu all reached the third-round with straight sets victories on Friday.
(Reporting by Rory Carroll; Editing by Ken Ferris/Peter Rutherford)
