Clijsters is on a winning streak after taking the Cincinnati title last week
Fifth seed Kim Clijsters needed three sets to beat American Bethanie Mattek-Sands at the Rogers Cup in Montreal.
The reigning US Open champion battled through 4-6 6-4 6-3 in two hours and 14 minutes for her sixth win in a row.
"I'm happy with the way I fought and just raised my level towards the end," said the Belgian.
Second seed Caroline Wozniacki beat Patty Schnyder 7-5 7-5, while Elena Dementieva, Francesca Schiavone and Victoria Azarenka also went through.
Defending champion Dementieva, seeded fourth, swept past Czech Klara Zakopalova 6-2 6-4, French Open champion Schiavone beat Ekaterina Makarova 6-4 6-7 (5-7) 6-2 and 10th seed Azarenka saw off Maria Kirilenko 6-4 6-1.
World number two Wozniacki had to work hard for a 7-5 7-5 win over Swiss veteran Patty Schnyder.
"Patty is a great player, she is a very serious player," said Wozniacki. "She knows how to play the points the way you don't like it, she likes to mix it up and she doesn't give you any rhythm.
"It's very difficult to play against a player like that."
Dinara Safina enjoyed her first back-to-back wins since January after she defeated 18th seed Nadia Petrova 7-5 4-6 6-4.
Ranked number one in the world this time last year, Safina has since struggled desperately with a back injury and slipped to 70 in the world rankings.
"Winning a three-set match, it's the first time in a long time," she stated. "It was about hanging in there and keep on fighting.
"We both played very good but I won. That is the nicest thing at the end of the day."