The No.23 seed ousted defending champion and World No.1 Naomi Osaka in 65 minutes to advance to the quarterfinals of the BNP Paribas Open, 6-3, 6-1.
It was a first win over a top-five player for the 19 year old, who is ranked 61st in the world. Bencic, ranked 23rd in the world, defeated Osaka 6-3, 6-1 to reach the quarter-finals of the prestigious WTA premier mandatory event, where Osaka won her first tour title previous year.
"I just kind of realized there's nothing else I'd rather do and I'm privileged to be here in the first place, so I might as well enjoy every step of the way", said Osaka, who won her first WTA title in Indian Wells past year.
Next up for Vondrousova - who ensured two teenagers reached the Indian Wells quarters for the first time since 2009 following Bianca Andreescu's upset of Wang Qiang, which set up a match against Garbine Muguruza - is Elina Svitolina.
Bencic will face either Karolina Pliskova or Anett Kontaveit in the quarter-finals of the WTA Premier event.
But there were no tears on Tuesday as Osaka said she was adjusting to being the world number one and always having a target on her back. "I was just fighting for every point".
"I think it's always a bit tricky whenever you change someone in the team, but I feel like for a first tournament we did really well", she said of her partnership with Jenkins, a former United States collegiate star who served as a hitting partner to Venus Williams from 2015 until the end of last season.
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The women's field lost its top two seeds as Romania's Halep, the 2015 Indian Wells victor, fell to Czech teenager Marketa Vondrousova 6-2, 3-6, 6-2.
Halep, who received medical treatment for blisters on her foot during the match, won less than half of her first-service points and hit just six winners to go with 36 unforced errors.
Osaka was also in Dubai, but lost her first match in the second round to Kristina Mladenovic, resulting in an emotional press conference where she admitted to struggling with her new position as the leading player of women's tennis. She rallied past Andrea Petkovic in the opening round and followed up by outlasting No. 3 seed Petra Kvitova in a third-set tiebreaker.
"I just got unlucky, got a virus somewhere and that's how it is".
Seven-time grand slam victor Venus Williams also found it tricky facing fellow American Christina McHale for the first time, but she pulled back early breaks in each set to win 6-2, 7-5.
Osaka conceded she didn't play well, but she didn't find the lopsided scoreline depressing because "I tried my best and I don't really have any regrets".