Wozniak, fresh off a loss in the second-round of Olympic play to eventual gold medalist Serena Williams, battled to a 7-5, 7-6 (7-5) win over Hantuchova, who lost in the third round of the Summer Games to Danish star Caroline Wozniacki.
The top seeds in the tournament take the court at Uniprix Stadium later in the week.
Top-seeded Victoria Azarenka, the Olympic bronze medalist, will face Paszek of Austria in her first match. Paszek earned a shot at the world No. 1 by knocking off Julia Goerges of Germany Tuesday 6-2, 6-1.
Other winners Tuesday were Roberta Vinci of Italy, Ksenia Pervak of Kazakhstan and Carla Saurez Navarro of Spain.
Celebrity Families of 2014 [PHOTOS]