After winning in 82 minutes, Australian Open champion Osaka will face Belinda Bencic for a spot in the quarter-finals after the 23rd seed defeated Ekaterina Alexandrova 6-4 6-2.
Halep's loss ensured Osaka will retain her number one ranking after the tournament.
"You are more relaxed, I think because you know that it's not the most important thing if you win the match or lose the match, and you have another chance the next week".
"I was trying to adjust, especially with my movement at the end of the first set and beginning of the second, and I think that was the key to coming back".
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".
Halep responded after losing the opening set, dropping just three service points to level the match in fine fashion. I'm hitting the ball well. "It's just really exciting to come out here every day and for everyone to be so kind".
"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", Osaka said.
Venus Williams beat Christina Mc Hale to reach the Indian Wells fourth round. AP
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 got injured during the match and received treatment for blisters on her foot. "She won everything in the past couple of months", Bencic said. "But it's everything I could do today".
It is the first time Vondrousova has beaten a top-five player.
The 21-year-old Japanese had a shaky start when she was broken early in the first set but quickly found her groove and broke the American four times and struck 29 winners to advance.
In-form Swiss Bencic blitzed the top seed, who surprisingly relinquished her crown following 28 unforced errors and just 10 winners. Venus Williams reached the quarterfinals with a 6-4, 6-4 win over Mona Barthel.
The 19-year-old, ranked 61st in the world, beat the Romanian 6-2 3-6 6-2.
Spain's Muguruza, a two-time Grand Slam champion now ranked 20th in the world, out-lasted seventh-ranked Kiki Bertens 5-7, 6-1, 6-4 while Williams, a seven-time Grand Slam victor, beat Germany's Mona Barthel 6-4, 6-4. Williams will fight for a semi-final berth against eighth-seeded Angelique Kerber, who beat ninth-seeded Aryna Sabalenka of Belarus 6-1, 4-6, 6-4.
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