The No.6-ranked Gauff, who saved a set point when trailing 5-4 in the first set, will play Katie Boulter of Britain, who advanced by beating American Taylor Townsend 6-4 6-4.
Gauff is playing in Beijing following her recent split from coach Brad Gilbert after more than a year and one Grand Slam title together.
That break-up came shortly after Gauff's defence of the US Open title she won in 2023 ended in a fourth-round loss against Emma Navarro.
Four-time major winner Naomi Osaka rallied from a set down to beat Yulia Putintseva 3-6 6-4 6-2. Osaka will play American Katie Volynets in the third round.
Chinese wild card Zhang Shuai, who ended a 24-match losing streak in singles lasting nearly two years in the first round, upset sixth seed Navarro 6-4 6-2, while 12th-seeded Diana Shnaider beat former Australian Open winner Sofia Kenin 6-2 6-3.
France's Caroline Garcia, whose ranking has slipped to 36, announced she is bringing an early end to her season because of shoulder and mental health issues.
Garcia wrote on Instagram: "This year, my mindset was toxic. I lost touch with the joy of being a tennis player and became obsessed with rankings and wins.
"I'm exhausted from the anxiety, the panic attacks, the tears before matches. Lately I've felt overwhelmed on tour - the pressure to perform, the eyes watching your every move.
"Winning doesn't feel fulfilling any more, it just brings relief that it's over. Yet, despite it all, I love tennis. So I'm choosing to step away for now. I'm taking a few weeks off to recharge then I'll start preparing for 2025 early."
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