The British number three took one hour, 33 minutes in Quebec to beat the wildcard Canadian who is 10 years her junior.
Watson had to fight back from a break point in the opening game and it took three set points to close out her younger opponent.
Parmentier claims Quebec City title for second win of year
The teenager continued to apply pressure in the second set and, despite being broken for a second time in the fifth game, managed to fight back from match point in the ninth before breaking her opponent to force another game.
The unseeded Briton duly returned the favour in the 11th game and served out the set for the win, leaving a match with either Georgina Garcia Perez or Rebecca Marino waiting in the quarters.
Naomi Broady’s tournament did not last long after she was earlier soundly beaten by top seed Petra Martic.
Broady, currently the British number four, was downed 6-1 6-1 by the Croatian, who is ranked 38 in the world.
Broady won the first game of the match, but things went badly after that as second-seed Martic reeled off 11 games in a row and won in only 56 minutes.
Elsewhere Monica Puig booked her place in the quarter-finals after Madison Brengle was forced to retire due to injury.
The number three seed was down 5-1 when Brengle’s problems began and the Puerto Rican took the next nine games back-to-back.
The American retired in the second set with a right hand injury with the score at 7-5 3-0 in Puig’s favour.
Also on Wednesday, teenager Amanda Anisimova made a splash at the Japan Women’s Open after taking out Zheng Saisai to reach her first WTA quarter-final.
The 17-year-old American beat the experienced Chinese, who is seeded seventh in Hiroshima, 6-1 6-1.
Australian Ajla Tomljanovic also made the last eight after she downed Zhu Lin 7-5 6-4.
Luksika Kumkhum of Thailand was on the way to booking her spot as she led Qiang Wang 7-5 3-2 when play was abandoned for the day.
Broady comfortably beaten by top seed Martic in Quebec
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