The world number one from Belarus recorded a 6-3 6-3 success in Beijing, although it was not as comfortable as the scoreline may have suggested.
"I didn't expect her to be that aggressive - she's always trying to take control, but she was really going for every shot," Azarenka said on www.wtatennis.com.
"She was pretty successful. I have to say it was quite challenging in a few rallies to turn it around and be aggressive, be demanding, be controlling - it was a challenge for sure.
"I had a few match points and really couldn't convert them. So when I won that last point, I was relieved to finish in two sets."
Joining Azarenka in the last eight was second seed Maria Sharapova, who dropped just two games on her way to a 6-0 6-2 triumph over Slovenian qualifier Polona Hercog.
Fifth seed Angelique Kerber got the better of 10th seed Caroline Wozniacki, getting her game together to take a see-saw encounter 6-1 2-6 6-4.
Home favourite Li Na, the seventh seed, also progressed through but needed to come back from a set down to defeat Chinese compatriot Shuai Peng 4-6 6-2 7-6 (7/3).
In the men's competition there were second-round wins for Mikhail Youzhny over Kevin Anderson (6-3 6-3) and home favourite Ze Zhang, 6-4 3-6 6-4 over fifth seed Richard Gasquet.
Feliciano Lopez progressed with a 6-3 7-6 (9/7) win over Yen-Hsun Lu, as did Sam Querrey who beat Andreas Seppi 6-1 6-4.