The Japanese 13th seed and WTA ranked 14th raced through the first set but had to work hard in the second on Rod Laver Arena before eliminating the 54th-ranked American 6-0, 6-4 in 65 minutes to make the third round.
"I remember when I was younger, I would watch her play in the pro circuit, and she was kind of notorious for getting every ball back," she said of Brengle.
"So I just kind of took those memories from back then and tried to tell myself, you're probably going to make a lot of unforced errors this match, but it's something you have to do because you can't let her dictate you in this match in the way that she would try to, like, keep the ball in play.
"For me, I feel like it was really important that even though I made a lot of errors at the net today, I thought it was really important to keep stepping in."
Osaka will meet another unseeded American next after Amanda Anisimova upset Tokyo Olympic champion and 22nd seed Belinda Bencic 6-2, 7-5.
Anisimova is on a seven-match win streak after claiming the Melbourne Summer Set title in the build-up to the Grand Slam and should pose a sterner test.
But if Osaka can win she faces the prospect of a mouth-watering fourth-round battle with world No 1 and Wimbledon champion Barty, who has dropped just three games so far and looks in ominous touch.
The pair could meet early due to Osaka's seeding – her lowest at a Slam since the 2018 US Open – after a truncated 2021 when she took time out to deal with mental health issues.
"I'm just trying to take it one day at a time," she insisted. "The goal for me is just to have fun and I'm really grateful to my team because I feel we are accomplishing that."
The four-time Grand Slam champion, who has won two of the past three Australian Opens, wasted little energy on Brengle in the first set.
She immediately broke to take control and raced through in just 20 minutes, with her opponent hitting zero winners and managing just 10 points.
Laughing and smiling on court, Osaka held serve to open the second set before Brengle won a huge round of applause by finally getting on the scoreboard for 1-1.
It lifted the American and Osaka faced a harder fight, with her unforced error count mounting.
But the Japanese star regrouped to secure the win.