The seventh-seeded Bouchard was the only woman to make it to at least the semifinals at each of the year's first three Grand Slam tournaments.
At Wimbledon, she became the first Canadian to appear in a major singles final.
To get to the quarterfinals at Flushing Meadows, Bouchard will need to beat No. 17 Ekaterina Makarova.
Zahlavov Strycova fell to 1-28 in matches against opponents ranked in the top 10.
After breaking to get to 4-all in Saturday's third set, Zahlavov Strycova double-faulted to fall behind 5-4. Bouchard then served out the victory.