The 19-year-old from Montreal is the first Canadian since Patricia Hy-Boulais at the 1992 US Open to get this far at a major.
Seeded 30th, the victory could move Bouchard to as high as 21st on the WTA rankings. The last Canadian to rank in the Top 30 was Aleksandra Wozniak (week of October 26, 2009 on 30th).
She overcame a slow start to eventually earn the victory in 100 minutes and set up a match with former world No.1 Ana Ivanovic on Tuesday.
"I'm feeling a lot of support from Canada," said Bouchard, who ended with six aces, 28 winners and six breaks of serve. "I'm excited to keep going and getting better.
"I tried to stay calm after the first set and focus on what I have to do in the point. I felt I started to play well. I stayed in the moment after a shaky first set and felt pretty good out there."
Bouchard said she watched some of Ivanovic's upset of Serena Williams.
"Ana plays aggressively and I'm looking forward to doing the same," she said. "No one's going to give it to me, so it's going to be a good match."