Bouchard prevailed 4-6, 6-1, 6-4 win over Israel's Shahar Peer, who has been ranked as high as 11th on the women's tour but has fallen back in recent months.
The 19-year-old Bouchard will have to stage a massive upset to make it to round three.
Bouchard faces world No. 2 Maria Sharapova on Friday.
"She is my idol, and I look up to her, especially her game style, I try to play like her, " Bouchard told CBC's Daybreak Montreal in December.
"To be compared to her is really special and I hope I can make those comparison more real and do as well as she has done," she added.
Bouchard in her first full year on the pro circuit after winning Wimbledon as a junior, the first Canadian to win a junior singles Slam.
She has been working with Nathalie Tauziat, a former Grand Slam finalist as a pro.
In other women's play, Russia's Svetlana Kuznetsova, the 2006 champion, beat Lourdes Dominguez Lino of Spain 6-3, 6-3 and 17-year-old Victoria Duval, a wild-card entry ranked 376th, beat 66th-ranked Andrea Hlavackova of the Czech Republic 7-6 (4), 6-4.
James Blake advanced to the second round in the men's draw with a 6-2, 6-2 win over fellow American Ryan Harrison on Wednesday night.
Blake, a former top-10 player now ranked 95th and playing on a wild card entry, was far more active than the 20-year-old Harrison in the 57-minute match.
Harrison won his first two service games to take a 2-1 lead, but Blake won the next five games to take the first set. In the second set, Blake raced to a 4-1 lead.
Two-time Grand Slam winner Lleyton Hewitt also won his opening match, topping Joao Sousa of Portugal 6-1, 7-6 (3).
Hewitt, the 32-year-old Australian who once topped the world rankings, made his first start in the event since 2009.
He has been injured much of the past three years, undergoing hip surgery and operations on his left foot, and is now ranked No. 91.