The sixth-seeded Zahlavova Strycova was pushed in the first set, as she had a set point against her on her own serve at 5-4 but after forcing a tie-break took control for a 76(2) 61 victory.
"The first match is always difficult," Zahlavova Strycova said. "I was a little bit nervous the first set. I wasn't playing the way I wanted to play. But I'm happy that I managed to get through."
Zahlavova Strycova, whose triumph here last year is her lone WTA singles title to date, came into this event on a six-match losing streak.
"It's good to be back again," Zahlavova Strycova said. "It feels very nice. It feels like home. I love this tournament and that's why I keep coming here."
The best hope for a Canadian titlist this year probably sits with No.4 seed Aleksandra Wozniak, who came into this week ranked 42nd, her highest rank since April 2010. Wozniak, who made her WTA qualifying debut here in 2002 and including qualifying outings is making her ninth appearance this year, was a 62 46 63 winner over Elena Vesnina.
"I'm excited to play here again," Wozniak said. "I was playing an opponent who plays like me, offensive tennis. We had some really good points. Playing indoors you have to adjust your game because the points are shorter. You have to go for more winners and mix it up a bit when you have the opportunity. It wasn't easy. Overall, I'm happy I'm through to the second round.
"It's nice to hear the encouragement from the fans. They helped me focus and stay motivated to win points."
Next up for Wozniak is Melanie Oudin, who from 5-3 down in the first set won seven straight games and had a set point against her in the second set tie-break of her 75 76(6) defeat of fellow American Irina Falconi. Now 3-0 against Falconi, Oudin also has fond memories of Québec City, having reached her first career quarterfinal here in 2008.
Also advancing were seventh-seeded Petra Martic and eighth-seeded Lucie Hradecka. Martic rallied from a 5-2 second set deficit in her 64 75 win over Jessica Pegula. Hradecka was a 64 76(5) winner over Maria Sanchez.