Sabalenka needed just 54 minutes to see off China's Xinyu Wang 6-1, 6-3 in their second career meeting and book her place in the Round of 16.
"She's a tough opponent and to get this win in straight sets, under an hour, it's an insane result and I'm so happy to be through," Sabalenka said afterwards.
"I think I really trusted myself, I was going for my shots without overthinking, and I think that was the weapon of tonight's match. I'm super happy I was able to stay focused and to be there in every point."
Sabalenka broke serve four times to book a fourth-round match against unseeded Czech Sara Bejlek in what will be their first career meeting.
Meanwhile, Gauff secured her spot in the fourth round courtesy of a 6-1, 7-6(3) win over fellow American Ann Li.
"Honestly, today was a little bit tougher for me coming from night to day, trying to control the ball a little bit, but overall I'm happy with how I played," said Gauff, who needed just 29 minutes to claim the opening set.
"Ann's not an easy opponent to play. She has a lot of variety in her game so I'm happy to get through."
Elsewhere, world number nine Elina Svitolina has withdrawn from the Cincinnati Open ahead of her third-round match against Wang Xiyu because of a right ankle injury.