Cibulkova was looking to avoid a repeat of her opener last week in Stanford, where she fell to WTA Rising Star Garbiñe Muguruza.
It appeared it would be smooth sailing when she rolled through the first set, but Abanda got the Canadian crowd fired up when she broke Cibulkova three times in taking the second set. However, the Slovak recovered her form and dominated the third set en route to a 6-1, 3-6, 6-0 victory.
"I had a really tough draw last week in Stanford," Cibulkova said. "I was hoping to get more matches in, but I didn't. I went into today's match really focused. I knew she's a young player, had nothing to lose and had all the support. After the second set, I knew what I had to change. I wasn't losing my head or panicking. That was important."
Abanda was proud of her performance in just her second WTA main draw event.
"I think I played one of my best tennis matches tonight in Montréal in front of my home crowd," Abanda said. "I'm really glad I was able to deliver in the second set. I'm excited to know that I can actually compete against a top player, so it's just more motivation for me to keep training and doing better."
Qualifier Yulia Putintseva fought off three set points in the first set and went on to a 7-6(5), 6-3 defeat of No.12 seed Flavia Pennetta. Putintseva's last WTA outing, a quarterfinal showing in Bastad, was her best. And this outing has already resulted in the best win of her career, as Pennetta is No.14 in the world, and Putintseva had never previously beaten a Top 30 player.
In an upset on paper, but not a huge surprise, Sabine Lisicki was a 6-1, 7-5 winner over 13th-seeded Sara Errani. The big-serving German broke serve five times and saved eight of 10 break points on her own serve.
Other victors included Alizé Cornet and WTA Rising Star Sloane Stephens. Cornet beat Lauren Davis, 6-3, 7-5, for her first win since upending World No.1 Serena Williams at Wimbledon. Stephens cruised past Canadian wildcard and 2012 Rogers Cup quarterfinalist Aleksandra Wozniak, 6-3, 6-0, for her third straight win in their head-to-head.