Garcia is currently ranked 89th on the WTA's singles standings, while Bouchard is No. 19.
The Canadian only saved three of her 10 break points compared to Garcia's 7-of-12 conversion rate. Bouchard had two aces compared to Garcia's three.
Also in the women's tournament, top-seeded Dominika Cibulkova of Slovakia, defeated New Zealand's Marina Erakovic to move into the semifinals.
China's Shuai Zhang beat Croatia's Ajla Tomljanovic 6-1, 5-7, 6-2, while American Christina McHale topped Estonia's Kaia Kanepi 6-1, 2-6, 6-4.
On the men's side, top-seeded David Ferrer withdrew from his quarter-final against South Africa's Kevin Anderson in the second set with a left leg strain.
Third-ranked Ferrer was leading 6-4, 2-2 when he suffered an inner thigh strain in his left leg. After seeking treatment in the locker room, the Spaniard returned to the court but lost the next two points before retiring.
Ferrer said he will have an MRI on Friday and then assess his recovery.
"I'm very sad because I was playing great", Ferrer said. "I still do not know the extent of the injury.
"I'll have to wait and see before taking a determination. The day was going so well for me and then this happened".
Anderson will next play Ukraine's Alexandr Dolgopolov, who defeated Ivo Karlovic of Croatia, 6-4, 7-6 (4). Anderson, who last week lost the Delray Beach final, will be playing in his first semifinals of an Open 500.
"It's unfortunate to win a match like this, but hopefully he gets better", Anderson said after the match. "I talked to him and he said that it happened when he was trying to go for a ball and felt his leg tweak a little bit".