The 25-year-old Pole will face Russia's Diana Shnaider for a place in the semifinals.
Earlier in the tournament, Świątek defeated Sara Bejlek of the Czech Republic and Viktorija Golubic of Switzerland.
The Canadian Open is a combined women's and men's hard-court tournament held annually in Toronto and Montreal.
In the men’s tournament, Poland’s Hubert Hurkacz was eliminated in the third round by Botic van de Zandschulp of the Netherlands, losing 6-3, 6-7, 5-7 in 2 hours and 46 minutes on Friday.
Świątek, a former world No. 1, was eliminated in the third round of Wimbledon last month by Alexandra Eala of the Philippines, failing to defend her title in London.
(gs)
Source: PAP