The Montreal native rallied to defeat Galina Voskoboeva of Kazakhstan 5-7, 7-6 (5), 6-4 on Monday.
Bouchard fired 29 winners and broke her opponent's serve three times, coming back after losing the opening set and again in the third set after losing an early break.
She had 25 unforced errors and three aces.
"It was a tough battle," Bouchard said. "I didn't play my best but fought my hardest. I came close to losing but I was able to fight my way back. I'm happy for that."
Later Monday, Vancouver's Vasek Pospisil, ranked No. 99, beat 131st-ranked Marc Giquel of France 6-3, 6-2, 7-6 (3).
Bouchard lost the first set when she sent a backhand long, but took the second against the 88th-ranked Voskoboeva after nearly an hour as she rallied from a 4-0 deficit in the tiebreaker.
In the third, Bouchard went up a break only to lose it three games later on a forehand error. But she got the break back for 5-4 and served out to win a game later on the first of three match points.
"In the end I think I broke (Voskoboeva) down a bit," Bouchard said. "I know she has a bit of a temper and I could see that after she lost the second set. That didn't bother me, but it did give me energy.
"I was confident and calm and felt I could outlsast her — which I did."
Bouchard is playing in the women's draw for the first time after winning the junior crown last year.
Her win came despite her modest grass-court season, with the teenager winning one round in a lower-level event in Nottingham and one qualifying round at Eastbourne.
Bouchard will face former world No. 1 Ana Ivanovic of Serbia in the second round. The 12th-seeded Ivanovic defeated Virginie Razzano of France 7-6 (1), 6-0 on Monday.
"I'm looking forward to playing Ivanovic in the next round but I have to play better than today," Bouchard said. "I need to fight a lot. She's a great player and I'm excited to be facing her."
Pospisil used a dominant serve in his match, firing 25 aces. He also made 30 unforced errors to Giquel's 28.
After picking up the victory, Pospisil said he played "one of the better matches" of his career.
"I played great, every part of my game was sharp," he said. "I was pleased with my level of aggression, being able to stay relaxed and seeing the game really well.
"I was playing very fast and making (Giquel) uncomfortable."
For the 23-year-old Pospisil, this year marks his second time at the All England Club. He was eliminated in the first round in his Wimbledon debut last year.
Pospisil will face Mikhail Youzhny of Russia in the second round.