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No.15 seed Kerber was handed a banana skin tie of sorts against Zheng Qinwen and was made to work hard for her 6-2 5-7 6-4 victory against the rising Chinese star.
Zheng battled back with three breaks of serve in the second set to level up and led 4-1 in the decider, but her opponent dug deep to prevail in a time of two hours and 18 minutes.
Daria Kasatkina awaits Kerber, who had not previously won this calendar year, after the Russian beat Katie Volynets 6-4 4-6 7-5 earlier in the day.
Keys was also pushed all the way in her clash with Misaki Doi before coming out on top 6-4 3-6 6-1 to set up a meeting with Alison Riske in round three.
The Australian Open semi-finalist struggled in the second set after holding her serve throughout the first, though she had enough quality to see off her Japanese opponent.
Gauff had less trouble against fellow American Liu, advancing in a little more than an hour to reach the third round, the stage in which she was eliminated on her debut here last year.
She will take on former world No.1 Simona Halep on Monday (AEDT), the day she turns 18, in a rematch of their round of 16 showdown from Wimbledon three years ago.
Emma Raducanu and Iga Swiatek are among the others already through to the Round of 32 in California.