Lucic-Baroni, the third seed, was beaten by American qualifier Danielle Lao 6-4 6-2 in the first round in Quebec City.
Lucic-Baroni beaten, Crawford survives in Quebec City
Mirjana Lucic-Baroni suffered a surprise loss at the Coupe Banque Nationale as Samantha Crawford survived a scare.
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The Croatian 2014 champion was outplayed by the 25-year-old, who is ranked 365th in the world.
The two other seeds featuring at the WTA International event on Monday advanced.
Crawford battled but got past Ysaline Bonaventure 7-6 (7-5) 6-7 (4-7) 6-4, while Evgeniya Rodina was too good for Jamie Loeb 6-2 6-2.
Talented American teenager CiCi Bellis, fresh from reaching the third round at the US Open, advanced with a 6-3 6-2 win over France's Amandine Hesse.
Alla Kudryavtseva overcame Veronica Cepede Royg 7-5 6-4 and Julia Boserup cruised past Amra Sadikovic 6-1 6-3.
Two local wildcards were beaten.
Carol Zhao suffered a 6-3 6-2 loss to Lauren Davis and Aleksandra Wozniak went down to Jessica Pegula 6-3 3-6 6-2.
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