It was a much easier passage for Iga Swiatek who powered her way past Marie Bouzkova, winning 6-1 6-1 against the Czech.
Osaka was back in the central Chinese city for the first time since 2017 and, in Tuesday's first match on centre court, facing the player who produced a major upset to beat her at the 2021 US Open.
Fernandez converted one of her two first-set break-point chances and served consistently.
But Osaka stepped up pressure on service returns in the second set, which featured five service breaks. She now plays Linda Noskova who beat Yulia Putinseva 6-4 4-6 7-6 (7-2).
Swiatek's victory was the six-time grand slam winner's 60th this year and the fourth year in a row she has reached that figure.
"Every tournament I go to, I want to play my best game," said Swiatek. "Sometimes I deliver, sometimes not, but, yeah, my expectation is to just do my best.
"Honestly, I don't set goals like semi-final or whatever — just really making it step by step."
The No. 2 seed will play Belinda Bencic or Elise Mertens in the next round.
Earlier Emma Raducanu retired ill from her first round match.
The British No.1 and former US Open champion had her blood pressure checked and temperature taken in her match against American Ann Li, retiring at 6-1 4-1.
American 14th seed Emma Navarro lost to Shuai Zhang 6-2 2-6 6-3 in the first round while fifth seed Mirra Andreeva was stunned by Laura Siegemund 6-7 (4-7) 6-3 6-3 in the second.
Sofia Kenin edged Anastasia Zakharova 3-6 7-6 (7-5) 6-3 to set up a second-round meeting with No.16 Liudmila Samsonova, who beat Emiliana Arango 6-1 7-5.
No.4 Amanda Anisimova, runner-up at the US Open and Wimbledon this year, withdrew from the tournament citing a left calf muscle injury after winning the China Open title on Sunday.
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