The 13th-seeded Canadian was down 5-3 in the second set but won the last four games to defeat France's Alize Cornet 7-6 (5), 7-5 in Monday's opening match on Centre Court.
Bouchard's victory set up a potential quarterfinal duel with Maria Sharapova, the former Wimbledon champion who beat her in the semifinals en route to the French Open title.
"This is what I've worked so hard for, to be in the quarters at Wimbledon," Bouchard said. "But I want to go another step. I want to keep going."
Bouchard, the only woman to reach the semifinals this year at both the Australian Open and French Open, became the first Canadian to reach the quarterfinals at Wimbledon since the Open era began in 1968.
"Another little historic thing for Canada," she said. "That's cool. I hope I can go further."
While Canada is making a breakthrough, with Milos Raonic playing in the men's fourth round Tuesday, American tennis was left with no player -- man or woman -- in the draw after John Isner lost and Madison Keys pulled out with an injury.
Most of the Bouchard-Cornet match was played under the Centre Court roof after rain stopped play with the Frenchwoman up 3-2 in the first set.
"Finally, I got to play under the very famous roof," Bouchard said. "Happy for that experience."
Cornet was coming off a three-set win over the top-seeded and five-time champion Williams in the third round Saturday but couldn't hold off the aggressive Bouchard.
The 19-year-old Keys withdrew from her uncompleted third-round match against Yaroslava Shvedova because of a strained left thigh. The match had been suspended by darkness Saturday with the Kazakhstan player leading 7-6 (7), 6-6.
"I came in this morning and I had lots of tape on and I tried," the 30th-ranked Keys said. "I had so much tape on me I could barely walk. It just wasn't happening."
The sixth-seeded Kvitova was a 6-3, 6-2 winner over Peng Shuai, No. 23 Safarova coasted to a 6-0, 6-2 win over 175th-ranked qualifier Tereza Smitkova -- another Czech -- and Zahlavova Strycova finally converted on her sixth match point to down No. 16 Caroline Wozniacki 6-2, 7-5.
Radwanska was a semifinalist at the All England Club in 2013 and was seeded fourth this year. Her exit means three of the tournament's four highest-seeded women are gone before the quarterfinals, joining No. 1 Serena Williams and No. 2 Li Na on the sideline.
Makarova is into the quarterfinals at Wimbledon for the first time, and now she will face Safarova.
Neither has ever been to a Grand Slam semifinal: Makarova is 0-3 in major quarterfinals; Safarova is 0-1.
Zahlavova Strycova, who has reached her first Grand Slam quarterfinal, served a six-month doping ban until April 2013 after testing positive for the stimulant sibutramine. She said Monday that she had considered quitting the sport during the suspension.
"I didn't want to come back and play again and compete," she said. "But it was just a short period of time. Like one month I was thinking like this. Then I was, 'Yeah, what I'm going to do?' I really like it. I love the sport. And then I didn't ask myself anymore."
The Associated Press contributed to this report.