The 18th-seeded Canadian wasted no time, opening up a 5-0 lead in 16 minutes. Bouchard, who reached the Australian Open semifinals this year, next plays either No. 14-seeded Carla Suarez Navarro of Spain or the unseeded Ajla Tomljanovic. They were playing later Sunday.
"I really believe in my skills. I believe I can play with the best girls out there," Bouchard said. "She's top 10, so I respect her. She can play some really good tennis. I was really mentally prepared for anything, for a battle. I think that mindset kind of helped me."
In the men's fourth round, Tomas Berdych routed No. 10-seeded John Isner 6-4, 6-4, 6-4. The sixth-seeded Czech next faces either 17-time Grand Slam champion Roger Federer, seeded fourth, or No. 18 Ernests Gulbis of Latvia. Federer won the first set against Gulbis, 7-6 (5), sealing the set with a forehand pass.
Kerber, a quarterfinalist at Roland Garros two years ago, made a string of unforced errors and Bouchard broke for a 2-1 lead in the second set when Kerber returned long from the back of the court.
"There is a lot of room for other players to move up," Bouchard said. "I think it just makes the draw really interesting when some of the top names are out and we see some new names that we haven't seen that much."
Trailing 5-2, Kerber played with the strings of her racket as she hunched forward on her chair, her head bowed. Bouchard, by contrast, sat upright, taking a few deep breaths to compose herself before serving out the match. She clinched victory on her first match point when Kerber — a two-time Grand Slam semifinalist — made another unforced error, this time as her wild forehand sailed out.
"I was not in the game. I was trying, but I had no rhythm," Kerber said. "I make so many mistakes. I actually was not moving very good."
In remaining third-round play, 12th-seeded Richard Gasquet lost 6-3, 6-2, 6-3 to No. 24 Fernando Verdasco of Spain. The Frenchman had a chance to break back to 4-4 in the third set, but sent a smash into the net as he was backpedalling. Verdasco then broke him before serving out the match.
Seventh-seeded Andy Murray defeated No. 28 Philipp Kohlschreiber, 3-6, 6-3, 6-3, 4-6, 12-10 in a match that was suspended on Saturday due to darkness with the score deadlocked 7-7 in the fifth set.