Play went on despite the lack of electricity, which shut down scorboards and umpires' microphones, and left the players without light or hot water in their clubhouse.
Bouchard, the rising star from Westmount, Que., suffered a power shortage of her own after walking onto centre court to a standing ovation.
The 20-year-old, perhaps rusty from not having played since reaching the Wimbledon final last month, couldn't make a shot in the first set, hitting normally routine shots long or wide.
The crowd went quiet watching as Bouchard's body language suggested she'd like to crawl into a cave and stay there.
Bouchard rebounded in the second set, hitting the crisp mix of shots that took her to at least the semifinals of the first three grand slam events this year. But nothing worked for her again in the third set.
The win put Rogers, a qualifier ranked 113th in the world, into the third round of the hard-court event. It also left the American 2-0 against Bouchard, who she beat in a lower-level tournament in 2011.
Earlier, Elena Vesnina stepped in as a replacement for the ailing Andrea Petkovic and posted a 6-4, 3-6, 6-2 victory over Camila Giorgi.
And former world No. 1 Venus Williams rebounded from a shaky second set to defeat Anastasia Pavlyuchenkova 6-1, 3-6, 6-2 in the first round if the hard court event.
The afternoon matches saw scoreboards go dark due to a long power outage that affected 200,000 Hydro Quebec customers in the area, but the matches went on uninterrupted.
Petkovic, the 16th seed, was unable to play because she was sick.
"I pushed it back until the end and really tried to get healthy," she said in a statement. "But I had a temperature and a fever and it's too risky to play like that in these kinds of conditions.
"I'm very disappointed."
She plans to rest in bed for two or three days and try to be ready for a tournament next week in Cincinnati.
Williams, who has played the Rogers Cup in Toronto before but never in Montreal, was on court in the early afternoon when the power went off.
"It was like going back to the southern California juniors," she said. "But I tried to think of it as positive, like 'this will be just like practice, so go ahead and relax. It will be a practice match.' You try to play those mind games when you're out there."
It was an even first round match, with Pavlyuchenkova ranked 24th and Williams 26th.
"We're both very good players and she's a dangerous player for the top players as well because she can do everything well when she's on," said Williams. "It felt good to win the match and hopefully gain some momentum for the rest of the week."
Williams is on the same side of the draw as her sister, top-seeded Serena Williams, who begins play Wednesday. They could not meet before the semifinals.
Serena Williams is to face Samantha Stosur, who beat qualifier Monica Puig 6-2, 6-2.
"I would love if we both got to the semifinals," said Venus. "I fell a little short last week (at Stanford), but that's why I'm playing these matches this summer. I'm getting better rhythm as I go."
Caroline Wozniacki, seeded 11th, had no trouble downing Daniela Hantuchova 6-1, 6-1. She is on pace to face Bouchard in the third round.
It was more trouble getting ready for the match in the dark.
"It's just so different: Everywhere, in the locker-room, it's so dark. We have to use our flashlights and phones. The water is freezing, as well."
In other matches, third seed Agnieszka Radwanska beat Barbora Zahlavova Strycova 6-4, 6-4, and 14th seed Carla Suarez Navarro defeated Bojana Jovanovski 6-4, 6-3.
Elsewhere, former U.S. Open champ Samantha Stosur defeated qualifier Monica Puig 6-2, 6-2 and Casey Dellacqua downed Kirsten Flipkens 6-0, 4-6, 6-2.
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