Gauff, who has not lost to anyone ranked lower than world number 22 Amanda Anisimova since the Australian Open, continued that impressive record by cruising past world number 62 Brengle, winning 58 per cent (34-of-59) of her return points in a dominant showing.
Anisimova, who eliminated Gauff from Wimbledon, also made it through her first match unscathed as she defeated hometown Canadian Carol Zhao 6-1 6-3.
China's Qinweng Zheng put another dagger into the Canadians with her 3-6 7-6 (7-5) 6-4 win over Rebecca Marino, but Bianca Andreescu gave the fans something to cheer for as she upset world number nine and winner of this past week's Silicon Valley Classic Daria Kasatkina 7-6 (7-5) 6-4.
Spain's Sara Sorribes Tormo prevailed against American Claire Liu 7-6 (7-4) 2-6 7-6 (7-5) in a three-and-a-half-hour battle of attrition, while Australian qualifier Ajla Tomljanovic upset world number 16 Veronika Kudermetova 6-4 2-6 7-6 (7-4) in two-and-a-half hours.
It was a disappointing showing from world number 10 Emma Raducanu as she went down 7-6 (7-0) 6-2 to the reigning champion of this event, Italy's Camila Giorgi.
Naomi Osaka also will need an early flight home after being forced to retire against Estonia's Kaia Kanepi, pulling the plug due to a persistent back injury while trailing 7-6 (7-4) 3-0.
In the late session, Olympic gold medalist Belinda Bencic successfully navigated the challenge of Tereza Martincova 6-4 6-2 to book a second round fixture against Serena Williams, and world number four Maria Sakkari survived a scare to finish strong and defeat Sloane Stephens 6-2 4-6 6-2.