Stephens used an accurate serve and steady pressure to rout Aleksandra Wozniak of Blainville, Que., 6-3, 6-0 while Cibulkova recovered from a mid-match stutter to down 17-year-old Francoise Abanda of Montreal 6-1, 3-6, 6-0 in opening round matches Monday at the US$2.44 million women's Rogers Cup.
Stephens, ranked 22nd in the world, was never in trouble against the 26-year-old Wozniak, who is trying to battle back to her career-high No. 21 ranking after years of arm and shoulder trouble.
"She really played well," Wozniak said of Stephens. "She served at a high percentage, 75 per cent, and it was tough to return.
"It wasn't easy, for sure. You have a warrior mentality, you want to fight for every point, but she played great tennis. I didn't expect that. She played a perfect match."
The 10th-seeded Cibulkova found herself in more of a battle than was predicted with crowd favourite Abanda, a rising junior talent.
Cibulkova advanced to a second round meeting with Britain's top woman player Heather Watson, who edged Tereza Smitkova 6-4, 5-7, 6-4 in a battle of qualifiers.
Abanda, ranked 209th in the world, had the crowd solidly on her side, and centre court was in a frenzy as the lanky junior used her strong ground strokes to the force errors from her 25-year-old opponent in the middle set.
"I think I played one of my best tennis matches," said Abanda. "Especially playing it in Montreal in front of home and the crowd, so I'm really glad I was able to deliver that in the second set.
"So I guess I'm just excited to know that I can actually compete against a top 10 player. It's more motivation for me to keep training and do better."
Cibulkova righted herself in the third set and sealed the victory with an ace.
"I knew she's young player, she has nothing to lose, she has all the support," said Cibulkova. "I just really had to calm myself.
"After the second set I just sit down and I talk to myself. I was playing well the first set, I knew what I have to change. I wasn't panicking. I wasn't losing my head. That was important."
There will be even more buzz for locals on Tuesday night.
American qualifier Shelby Rogers downed Ajla Tomljanovic 6-4, 7-6 (5) to set up a second-round meeting on Tuesday with the star attraction of this year's event, fifth-seeded Eugenie Bouchard of Westmount, Que.
"I think it will be fun," said Rogers, who beat Bouchard in three sets in a lower-level tournament in 2011 in Troy, Alabama. "Obviously the crowd is going to be for her, and I'm the underdog. I think it's kind of a fun story.
"There's no pressure. I'm just going to go out, play my game, do my best and try to enjoy the moment as much as I can."
Bouchard, who has rocketed up the rankings since turning pro full time in 2013 and who reached the Wimbledon final last month, is drawn to face defending champion Serena Williams in the quarter-finals.
Williams, who this week reached 200 straight weeks as world No. 1, said 20-year-old Bouchard will be a stiff test, if it happens.
"I think she has a really good chance," said Williams. "She's had a stellar year, to be honest.
"She's done better than me in a lot of the tournaments. Yeah, I think it will be a really good matchup. I hope I can get there. I feel like she'll be there regardless."
Williams, coming off a win Sunday at Stanford, has won the Rogers Cup three times when it was held in Toronto, but has not even played in Montreal since 2000, when she was forced to retire from the third set of the final with an injury.
She'll play her first match on Wednesday.
Lucie Safarova, the 15th seed, advanced with a 6-4, 6-2 win over Sorena Cirstea. She next faces Magdalena Rybarikova, a 6-1, 6-3 winner over Alison Riske.
Alize Cornet beat qualifier Lauren Davis 6-3, 7-5 and will next face eighth-seeded Victoria Azarenka.
Sara Errani and Roberta Vinci of Italy are the top doubles players on the WTA Tour, but both lost their opening singles matches.
Sabine Lisicki downed 13th-seeded Errani 6-1, 7-5 while Barbora Zahlavova Strycova ousted Vinci 7-5, 7-5.
Another Italian fell as Yulia Putinseva topped 12th-seeded Flavia Pannetta 7-6 (5), 6-3.
Errani and Vinci are ranked first in doubles, having taken Wimbledon and the Australian open titles this year.
But while Errani is 15th in singles, most of her success has been on clay courts, while Lisicki likes the faster surfaces. Lisicki hit the fastest recorded serve in WTA history of 211 kilometres per hour last week in the first round at Stanford, breaking Venus Williams' record.
Klara Koukalova beat Dutch qualifier Kiki Bertens 7-5, 7-6 (5).
Zahlavova Strycova advanced to a second-round meeting with third-seeded Agnieszka Radwanska.
After Abanda's match, a ceremony was held on centre court to induct Arantxa Sanchez Vicario into the tournament Hall of Fame.
The former world No. 1 reached the final of the Canadian Open, now called the Rogers Cup, five times between 1989 and 1998, winning twice in Montreal in 1992 and 1994.
"I know they were great finals," said the Barcelona native. "I definitely had to beat Steffi (Graf) and Monica (Seles). They were my biggest rivals at the moment.
"I remember the crowd was always behind me. I feel like at home here in Montreal. As I say, it was one of my favourite tournaments to come and play. In that era, I was probably one of the players that was doing really well in this tournament, and I was fighting to win the trophy. I have great memories."
The 42-year-old Sanchez Vicario lost to Martina Navratilova in the 1989 final in Toronto, then reached four straight finals in Montreal. She lost at Uniprix Stadium to Seles in 1996 and 1998
Sanchez Vicario piled up 29 tournament wins in singles and another 69 in doubles before retiring from tennis in 2002. She took four grand slam titles: the French Open in 1989 (as a 17-year-old), 1994 and 1998, and the 1994 U.S. Open.
She was named to the international tennis hall of fame in 2007.