Bartoli struggled with her serve throughout the match, giving away four double-fault points, while Voskoboeva capitalized on her opportunities by winning four of her six break points.
"It was a day when nothing was working," Bartoli said. "I tried my hardest but I committed so many mistakes it was hard to win. I was not feeling the ball and my legs were not moving. I was late on everything and committing a lot mistakes, especially on my backhand."
Bartoli was making her eighth appearance at the Rogers Cup and first since a first-round defeat in 2009 when she lost as the 13th seed to Ukraine's Alona Bondarenko.
"Something is not going well for me here in Toronto," Bartoli said. "I don't know if it is the surface or the humidity or something, but it's been a two-year gap and it's the same kind of match."
Goerges sailed through the first set against the former No. 1 with overpowering forehand winners from the baseline and an aggressive first serve.
It was the first match since Wimbledon for Jankovic and the Serbian showed rust.
"Obviously I had a hard time playing my first match since June," she said. "I wasn't feeling my game out there and hopefully with more matches I'll be better in my next tournament."
Romanian Simona Halep -- another qualifier -- rallied to upset 12th-seeded Svetlana Kuznetsova of Russia 4-6, 6-4, 6-3. The 15th-ranked Kuznetsova had 50 unforced errors to send Halep to the second round in her Rogers Cup debut.
In other matches, 10th-seeded Australian Samantha Stosur opened with a 4-6, 6-2, 6-3 victory over Japan's Ayumi Morita; China's Jie Zheng defeated Italy's Alberta Brianti 6-2, 6-1; the Czech Republic's Lucie Safarova downed Slovakia's Polona Hercog 6-3, 4-6, 6-3; Russia's Nadia Petrova ousted Australia's Jarmila Gajdosova 6-1, 6-2; and Hungary's Greta Arn upended the Czech Republic's Klara Zakopalova 6-3, 6-1.