The 25-year-old, who won her first WTA Tour title on Sunday, won 6-4 6-2 in one hour 21 minutes in Montreal.
The world number 14 will play either Hungary's Timea Babos or American Vania King in the next round.
Britain's Naomi Broady will face Spain's world number three Garbine Muguruza in the second round later.
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British number one Johanna Konta progressed to the second round of the Rogers Cup with a straight-set win over American Shelby Rogers.