Gauff's last defeat was in the quarter-finals in Montreal following her Washington triumph and the teenager has been an unstoppable force ever since, winning the Cincinnati title and her maiden Grand Slam crown at her home US Open.
The world number three outclassed Ekaterina Alexandrova in her Beijing opener and battled past Petra Martic.
She produced a determined display in the first set against Kudermetova to lay the platform for a second career win over the Tokyo champion.
"I'm really happy with how I've been able to manage. I had trouble finding the way I wanted to play in these conditions. I felt like the balls were flying in the first match and playing passive in the second," Gauff said.
"I'm really happy with how I've been able to troubleshoot and problem-solve. Today I played a good match overall."
Gauff next meets sixth seed Maria Sakkari (28) in what would be a rematch of their title clash in Washington.
Sakkari got past local favourite Wang Xinyu (22) 6-4, 2-6, 6-3.
"I think she's probably one of the most athletic players on tour so I think it's going to be tough," Gauff said.
Earlier, former champion Caroline Garcia (29) sealed a 6-3, 6-2 victory over Ukraine's Anhelina Kalinina (26) to set up a quarter-final clash with second seed Iga Swiatek (22).
Frenchwoman Garcia, who is ranked 10th in the world but a further 10 places back in the race to qualify for the season-ending WTA Finals which she won in 2022, has enjoyed a steady run of form in the last few weeks.
Garcia reached the quarter-finals in San Diego and Tokyo with a Guadalajara semi-final appearance in between.
World number one Aryna Sabalenka (25) later overcame a spirited Jasmine Paolini (27) 6-4 7-6(4) to set up a blockbuster meeting with former Wimbledon champion Elena Rybakina (24).
Sabalenka has a 4-1 record against the Kazakh, most notably defeating her in the Australian Open final, before losing their latest meeting in the Indian Wells title clash.
"I'll go out there tomorrow and do my best to get this win," Sabalenka said.