Japan's Osaka, whose second straight Grand Slam title at the Australian Open propelled her to the top of the rankings, traded breaks with Collins early in the first set.
But she got the decisive break in the ninth game, giving herself a break point with a backhand winner before pouncing on a short ball and belting a forehand winner to give herself a chance to serve for the set.
An increasingly confident Osaka broke Collins at love for a 2-1 lead in the second. She finished out the next game for a 3-1 lead and led 5-1 before Collins saved a match point to hold and make Osaka serve out the match.
Collins, trying to build on a breakout run to the Australian Open semi-finals, failed in her bid to avenge her 6-1, 6-0 loss to Osaka in their only prior meeting in Beijing last year.
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And Osaka, whose first career title came at this prestigious WTA premier mandatory event last year, advanced to a meeting with Bencic, the 23rd seed who defeated Russian Ekaterina Alexandrova 6-4, 6-2.
Bencic stunned two-time Wimbledon champion Petra Kvitova in the final at Dubai last month to capture her first WTA title in four years.
The 21-year-old stunned two-time Wimbledon champion Petra Kvitova in the final at Dubai last month to capture her first WTA title in four years.
She won the WTA title in Toronto in 2015 before a series of back and wrist injuries saw her slide down the rankings.
In other third-round action, three-time Grand Slam champion Angelique Kerber came from a set down to beat Russian qualifier Natalia Vikhlyantseva 3-6, 6-1, 6-3.
After dropping her serve in the first game of the second set, Kerber won seven games in a row to force a third set and take a 2-0 lead in the decider.
She was unable to convert four match points against Vikhlyantseva's serve at 5-1 and was broken at love when serving for the match at 5-2 before finally putting it away.
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"I think it gives me confidence that I can turn around matches, that I can play also three sets, also in the close moments that I'm there, that I can trust myself," said Kerber, adding that it was always difficult to face an opponent for the first time.
She'll be doing the same in the round of 16 against Aryna Sabalenka, the ninth seed from Belarus who defeated Lesia Tsurenko 6-2, 7-5.
Seven-time Grand Slam winner 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.
"I never played her, so you're out there learning what they do well, what shots they select," Williams said, adding that it wasn't until the second set that she felt 'OK, I understand.'
"I felt comfortable with trying to control the point from there," said Williams, who fired 20 winners and converted seven of her nine break point chances.
She'll fight for a quarter-final berth against Mona Barthel, a 7-5, 1-6, 6-4 winner over Julia Goerges in an all-German contest.
Fifth-seeded Czech Karolina Pliskova relied on a solid service game in a 6-3, 6-2 victory over Belgian qualifier Ysaline Bonaventure.
She next faces Estonian Anett Kontaveit, who was leading 5-0 against 11th-seeded Anastasija Sevastova when the Latvian retired from their match.
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