The British No. 3 made a winning start in Quebec City with a 6-4, 3-6, 6-3 victory over Australian teenager Destanee Aiava on Monday.
However the 27-year-old, who sits at 135 in the latest WTA rankings released on Monday, will have to give it her all in the last-of-16 round when she meets the 24-year-old Hungarian, who is currently world no. 63.
The Belgian -- who is 41st in the WTA rankings -- came through 7-6 (8/6), 6-1 in just over an hour-and-a-half against Russian Rodina.
Fourth seed Kristyna Pliskova of the Czech Republic also progressed after her 7-5, 7-5 win over Chang Kai-Chen of Chinese Taipei, while Alison Riske, the seventh seed, came from behind to defeat fellow American Madison Brengle 5-7, 6-3, 6-4.
Elsewhere, there were also first-round wins for Chinese pair Qiang Wang and Xinyun Han, while Slovakian Jana Cepelova advanced to the second round after Aliaksandra Sasnovich of Belarus retired, having lost the opening set 6-3 and being 1-0 down at the start of the second.