The eighth-seeded Crawford finally put the match away in just over two hours after Bonaventure saved two match points in the second set and forced the decider.
In other matches, 17-year-old Cici Bellis followed up her third-round showing at the U.S. Open with a 6-3, 6-2 win over France's Amandine Hesse.
Bellis reached a career-high ranking of No. 120 after winning three matches in qualifying in New York and then advancing to the third round, falling to eventual champion Angelique Kerber.
Another American, 365th-ranked Danielle Lao, upset 2014 Quebec City champion and third-seeded Mirjana Lucic-Baroni 6-4, 6-2 in a late match.