Tauson, seeded 16th in the hard-court event, avenged a loss to Swiatek at Wimbledon, where she lost 6-4, 6-1 after struggling with illness in her straight-sets loss.
The 22-year-old Tauson used her creativity and firepower to frustrate the six-time Grand Slam champion from Poland, staying calm when she was broken in the second set and sealing the win when Swiatek's backhand landed in the net.
"It's tough conditions here with the wind, but I tried my best to keep my head cool and keep working," Tauson said in her on-court interview.
"Even though I got broken in the second set, I was feeling confident and I'm really happy about the win."
Swiatek's loss came a day after top seed Coco Gauff was stunned in straight sets by Canadian teenager Victoria Mboko, and both Swiatek and Gauff will look to sharpen their games ahead of the start of the U.S. Open later this month.
World number one and U.S. Open defending champion Aryna Sabalenka is not competing in Montreal.
Tauson, seeded 16th, will face Madison Keys in the quarterfinals after the big-serving American saved two match points to emerge with a hard-fought 4-6 6-3 7-5 win over Czech Karolina Muchova.
Tauson beat Keys in their only previous meeting in Auckland in January. Keys went on to capture her first Grand Slam title at the Australian Open later that month.
Tauson won her only tour title in New Zealand in January, beating fellow Montreal quarterfinalist Naomi Osaka of Japan in the final