De Minaur, seeded third, hasn't lost to a fellow Aussie in four years, but he was made to work hard by his 86th-ranked compatriot to keep that streak alive.
The second-round match turned in an instant in the second-set tiebreaker when a return which rolled off the top of the net handed de Minaur a match point after he saved six set points for his opponent.
"A little bit of luck went my way in the tiebreaker," de Minaur said. "He was hitting me off the court in the second set, but I got lucky and managed to sneak away with the tiebreaker.
"Ultimately it was a lot of fighting and competing," added de Minaur, the 2023 runner-up in Canada who married British WTA player Katie Boulter last month.
De Minaur said he hasn't given much thought to his solid recent record against fellow Aussies.
"We're doing our best to make Australia proud," he said. "We have strength in numbers."
In other second-round action China's Shang Juncheng - only just returned from months away because of injury - scored the first notable upset of the week with 7-5, 4-6, 7-6 (5) defeat of 10th seed Andrey Rublev.
Shang saved five match points, on his way to the third round, breaking Rublev as he served for the match at 5-3 in the third and hanging on to win a seven-deuce service game.
Former world number three Stefanos Tsitsipas regained some of the touch lost during a recent rankings slump, with the high-profile qualifier dispatching Martin Damm 6-4, 6-4.
The 98-minute first-round win sends Tsitsipas into a match with Brazilian Joao Fonseca.
The 53rd-ranked Tsitsipas, winner last month in Gstaad, said that a coaching change - he split from his father Apostolos for a second time - is paying off now that he is under the guidance of coaches from Patrick Mouratoglou's French academy.
Buddhist philosophy
"It's a chapter that should have started a long time ago," Tsitsipas said. "I guess I was too patient with my time and too nice with handling certain things, to take so much time to proceed with the change. But it's how life works."
"Certain things come at a certain time, I'm very Buddhist in that sort of philosophy.
"Now we are here, and we are doing it the way I like it. I want it to be done. I want it to be done with a coach that I am happy with right now ... someone that I trust."
The Greek claimed the opening set against Damm and came back from a break down in the second to earn a 5-2 lead and the chance to serve it out.
But the Czech managed to break back, forcing Tsitsipas to clinch victory two games later on a forehand winner.
"I need to focus and concentrate, and that's what I was trying to do out there today, trying to keep it locked in as much as I could and not let any distractions get in the way," Tsitsipas, 27, said.
"Tennis is about milliseconds, getting properly behind the ball and being constantly well positioned. I need to focus on how to do that in the best possible way.
"I felt in control up two breaks, but things got tough. I have nothing to regret, I was able to fight my way through the match. I took a good grip to close it out."
Hubert Hurkacz a 2022 finalist in Montreal who is coming back from a knee injury suffered at Wimbledon, returned with a 7-5, 4-6, 6-2 win over Marcos Giron.
Britain's Jakob Fearnley, who reached the final of a hard court Challenger last month, advanced past French veteran Adrian Mannarino 7-6 (3), 6-4, overcoming more than 30 unforced errors to book a meeting with 13th seeded Czech Jakub Mensik.
Fellow Brit Jack Draper shed bitter tears as his latest injury comeback collapsed in a 6-3, 2-6, 6-2 loss to France's Terrance Atmane, who delivered an ace on match point.
Draper, who had not played a match since Eastbourne in June, was consoled at the net by his victorious opponent.
It was more disappointment for Draper after he and new coach Andy Murray travelled to last week's Washington event only for Draper to withdraw as an existing arm injury flared up.
Canadian Denis Shapovalov, who reached the final in Los Cabos at the weekend, was disappointed to retire with an ankle injury to hand a 4-6, 6-4, 3-0 victory to Zachary Svajda.