The sixth seed from Belarus, coming off a shoulder injury, advanced past the hometown hero after two hours and 23 minutes into a last-16 match against China's Wang Yafan.
"I think my mindset was the key today for the victory," Azarenka said. "I knew it was going to be some ups and downs, I would have to adjust in some moments. I also know she's a very talented player. She didn't give me much of the rhythm."
Azarenka could meet compatriot and two-time reigning Australian Open champion Aryna Sabalenka in the quarter-finals if the world number three defeats Russia's Kamilla Rakhimova after a first-round bye.
Azarenka, like Sabalenka, withdrew from Wimbledon due to a shoulder injury.
"It was good for me to test my shoulder today," she said. "It went well, so I'm pretty happy with that."
Former world-number-one Azarenka, who beat Baptiste in their only prior meeting at Chicago in 2021, said she never felt comfortable during the match.
"It was hard for me to expect a high level of tennis after having a break and coming off from injury, not really having too much time on the practice court," Azarenka said.
"But I feel like I fought really hard. In the tie-breaks, in the important moments, I really executed well and did what I wanted to do. I'm very happy with that aspect, that when it did count, I really was able to step up my level."
Just a week ago, 20th-ranked Azarenka was uncertain she would play in the US capital.
"I've been trying to pace myself after the injury. I wasn't sure if I'm going to be ready at all," said Azarenka. "Middle of last week I was, 'How in the world am I going to play in Washington? I have no idea.'
'Doubts'
"This was my first time actually playing two sets. Even in practice I still wasn't able to pick up that much tennis. Definitely it was kind of getting back into that match swing. I've practiced a lot, hours of fitness and stuff, but the matches are different."
Azarenka, the 2012 and 2013 Australian Open champion who turns 35 on Wednesday, was trying to recover confidence in her shotmaking after the lay off.
"After a break, you have those hesitations, you have some of those doubts. Sometimes the quicker decision-making is not as natural after not playing for a while," she said.
"I felt like I knew what I wanted to do and execution was a little bit on and off. It's something I need to clean up a little bit."
On the men's side, US fourth seed Sebastian Korda ousted Chile's Christian Garin 6-3, 6-2 to reach the third round and Canada's Denis Shapovalov advanced to the last 16 by defeating French sixth seed Adrian Mannarino 6-2, 6-1.
Another hometown favorite, fifth seed Frances Tiafoe, rallied to beat Colombia's Daniel Galan 6-7 (8/10), 6-3, 6-3. Tiafoe held at love in the final game, taking the last point on a service winner after two hours and 22 minutes.
