Ranked 175th in the world, the Vancouver player won 6-3, 3-6 and 6-2 ahead of Greet Minnen of Belgium, 103rd.
Marino had the advantage 4-2 for the breakages, in addition to having seven aces.
Marino will take part in a second major tournament this year after Australia in February.
Bianca Andreescu, Félix Auger-Aliassime, Denis Shapovalov and Vasek Pospisil will also represent Canada in singles, in New York. Milos Raonic skips the tournament, annoyed by a leg injury.
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