Seeded 28th, Brady dominated from the baseline to take leads of 4-0 in the first set and 2-0 in the second against Putintseva, who won their two previous meetings.

Brady said the fast start helped her calm down.

“I came out with nerves. I think she did, too,” Brady said. “I just tried to pretend it was a first-round match, and I was happy with the way I started. Then I was able to keep the momentum and build off of that.”

Brady’s opponent Thursday will be winner of Tuesday night’s match between two-time major champion Naomi Osaka and American Shelby Rogers, who is ranked 93rd.

Shapovalov plays tonight

Richmond Hill’s Denis Shapovalov, the 12th seed and lone Canadian remaining in the event, plays a men’s quarter-final later tonight against No. 20 seed Pablo Carreña Busta.

Brady, 25, is playing in her 13th Grand Slam event and is seeded in a major tournament for the first time. The native of Harrisburg, Pennsylvania, trained as a youngster at the Evert Tennis Academy in Florida and played for the UCLA Bruins on their 2014 NCAA championship team.

“She has come into her own right now,” said six-time U.S. Open champion Chris Evert, an ESPN commentator. “She has matured. Some players mature later on; some mature very, very young. This is her time right now.”

Brady has plenty of weapons, with powerful groundstrokes off both sides and a serve to match. She hit 22 winners to seven for Putintseva, and said she won by keeping rallies shorter than in their previous meetings.

“The last couple of times I played her, I got caught in playing her game,” Brady said. “I don’t think I’m better at her at running, so I definitely was a lot more aggressive today.”