Bouchard, the seventh seed of Canada, overcame a determined challenge from Barbora Zahlavova Strycova to progress 6-2 6-7 (2-7) 6-4 on Arthur Ashe Stadium.
Zahlavova Strycova, the 30th seed of the Czech Republic, broke in the first game of the match, but Bouchard claimed three breaks to coast to the first set.
Not to be denied, Zahlavova Strycova broke again early in the second, only for Bouchard to hit back for 2-2.
The pair exchanged more breaks as Zahlavova Strycova failed to serve out the set at 5-4, but showed composure to win a tie-break and force a deciding set.
Bouchard had the match on her racquet when she broke for a 4-3 lead, but she failed to consolidate it - much to her own amusement - as Zahlavova Strycova levelled for 4-4.
But in a tight ninth game which went to deuce, Zahlavova Strycova crumbled to hand Bouchard the break again - and the Wimbledon finalist served out the contest to love.
Bouchard will take on Russian 17th seed Ekaterina Makarova, who eased into the last 16 with a 6-2 6-4 win over Kazakhstan's Zarina Diyas.
Czech third seed Kvitova was ousted by Serbian qualifier Aleksandra Krunic 6-4 6-4.
Krunic, 21, will meet Victoria Azarenka in the fourth round, after the Belarusian - seeded 16th - thrashed Russia's Elena Vesnina 6-1 6-1.
Australian 29th seed Casey Dellacqua continued to set a new personal best effort for herself at Flushing Meadows, reaching the fourth round.
Dellacqua had previously never surpassed the second round, but her first match in the last-32 in New York was a winning one - as she downed Czech Karolina Pliskova 6-3 3-6 6-4.
Next up for Dellacqua is 11th-seeded Italian Flavia Pennetta, who dispatched of American Nicole Gibbs 6-4 6-0.
Top seed Serena Williams eased past fellow American Varvara Lepchenko.
The 17-time major winner will face Estonia's Kaia Kanepi in the last 16, after the latter upset Spanish 15th seed Carla Suarez Navarro 7-5 6-0.