This was just before her sister Serena withdrew from the competition due to back problems.
Serena, who was forced to retire from the Rogers Cup final on Sunday by back spasms, had been due to play Zarina Diyas in the first round.
After Venus and Bertens split the first two sets, Williams surged ahead 3-0 in the third, thanks to some excellent volleying.
But she struggled to put her opponent away, committing numerous errors when serving for the match at 5-3.
Bertens held at 5-5 and then forced a tie-break with an ace.
Williams, however, took control of the tie-break, moving ahead 3-0 and 6-2 before sealing the win.
“I just tried not to go too big, because I can go so big and I have a lot of power and it’s not always easy to control it,” Williams said.
“So, I’m trying to play smart instead of going hog wild, which is extremely easy to do.”
German 13th seed Angelique Kerber exited the tournament when she lost to Estonia’s Anett Kontaveit 7-6(7) 6-2.
The 23-year-old Kontaveit came from 5-3 down and saved a set point at 6-5 in the opener against the former world number one.
She broke Kerber twice to win the second set, winning the first nine points, and two holds to love gave her a 4-0 lead.
Swiss 12th seed Belinda Bencic retired with a foot injury when trailing Victoria Azarenka 6-4 1-0.
Former world number one Azarenka will face Donna Vekic in the second round after the Croatian beat Czech Katerina Siniakova 6-4 6-3.
American Madison Keys beat fellow big hitter Garbine Muguruza of Spain 6-7(4) 7-6(5) 6-4.
Russia’s Ekaterina Alexandrova wasted little time in beating Carla Suarez Navarro of Spain 6-4 6-1 in 56 minutes while China’s Zheng Saisai beat Viktoria Kuzmova of Slovakia 6-3 6-1.
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