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 failed to make it past the tournament's third round last year.
American Jennifer Brady defeated 19th-seeded Caroline Garcia 6-3 3-6 6-0 to punch her ticket to the third round.
Stephens powers past Gauff in All-American clash to reach third round
The 23-year-old Brady thumped five aces en route to her third victory over the French this year.
Czech Marketa Vondrousova eased past an error-prone Daria Kasatkina 6-2 6-1.
With the loss the 14th-seeded Kasatkina, who was a finalist at the tournament last year, is projected to fall out of the top 20 when rankings are released after the tournament.
Garbine Muguruza broke American Lauren Davis for a speedy 6-1 6-3 win to send the Spanish 20th seed into the third round and keep her dreams of a maiden title in Indian Wells alive.
US Open women
Raducanu impresses with first-round win over Vogele
Serena survives scare against Stephens as quest continues