The 37-year-old Williams has won the event three times, all in Toronto, and has a 31-4 match record.
“I feel like my movement is great. Been working on my fitness, so I felt like it really was able to shine through today,” Williams said. “I’m loving going out there, and I’m loving kind of running. So it’s a good thing.”
“Now that I’m just injury-free, I’m just enjoying being able to train, and I haven’t been able to do it since January, really,” said Williams, who is seeded eighth. “So I just think that the fact that I can train and practice and get in the gym is really going to be helpful for me.”
The winner last year in Montreal, Halep lost a 4-0 lead in the third set when Brady won five straight games. Halep broke Brady for the third time in the set to go up 6-5, but Brady broke back to force the tiebreaker.
“It was a very, very tough one,” Halep said. “I expected it because I knew that she’s going to serve big, and also the forehand is big. I didn’t feel 100 percent ready for the tournament because I had a long break [after Wimbledon]. But I’m really pleased with the way it was today, the fact that I fought ’til the end.”
Second-ranked Naomi Osaka of Japan reached the third round when German qualifier Tatjana Maria retired because of a left abdominal injury. Osaka led 6-2 in her first match since losing in the first round at Wimbledon.
Ukraine’s Elina Svitolina, the 2017 Rogers Cup winner, moved onto the third round with a 6-3, 3-6, 6-3 victory over Katerina Siniakova, and 2015 champion Belinda Bencic of Switzerland edged Julia Goerges 5-7, 6-3, 6-4. Bencic and Svitolina will face each other Thursday.