Ranked 36th in the world, Venus Williams endured three sets in her first two matches.
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 a year ago.
"Honestly, I think at a time like this with that scoreline, I would usually feel very depressed and sad", Osaka said.
"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. But I feel pretty good right now, because I tried my best and I don't really have any regrets.
"I haven't played that much, so I wanted to make it count", said Williams, who expects to play about 12 tournaments this year.
After her 66-minute triumph over Osaka, Bencic will fight for a semi-final berth against either fifth-seeded Czech Karolina Pliskova or Estonian Anett Kontaveit.
The victory over Osaka came in "very high" in her list of big wins. I think I played a little bit wrong.
"I played, I think, a great match. It's not going to get any easier from here, so I just have to continue to raise my game". I'm hitting the ball well. "So just things worked out for me", said Bencic.
Halep's loss ensured Osaka will retain her number one ranking after the tournament.
2015 champion Simona Halep suffered a shock loss at the BNP Paribas Open, at the hands of 61st ranked teenager Marketa Vondrousova. Halep got injured during the match and received treatment for blisters on her foot.
Bencic was the youngest woman to break into the top 10 since 2009 when she made the list in February 2016 as an 18-year-old, but a litany of injuries has stalled her progress.
She will next face Garbine Muguruza after the Spaniard battled back to dispatch Kiki Bertens of the Netherlands 5-7 6-1 6-4.
In Stadium 2, sixth-seeded Nishikori was stunned by Polish qualifier Hubert Hurkacz 4-6, 6-4, 6-3.
Andreescu - who roared to her first WTA final as a qualifier in Auckland in January, beating two former world number ones on the way - is in the quarter-finals of one of the WTA's elite premier mandatory events for the first time.
She will play either Ukraine's Elina Svitolina or Australian Ashleigh Barty in the last eight.