Andreescu, 19, who clinched her second professional title at the Women's Tennis Association Premier 5 event in Toronto, needed just one hour and 55 minutes to reach her first Grand Slam quarterfinals, reports Efe news.
The Canadian teen ended the game - held in the Arthur Ashe Stadium at Flushing Meadows - with 33 winners and 26 unforced errors but committed eight double faults, which cost her the second set.
Meanwhile, 23-year-old Townsend won only 16 of 40 net points and struck 25 winners while committing 24 unforced errors.
However, the American's serve was no match for Andreescu's returns from the baseline and she was always at the mercy of the rhythm set by the Canadian player, who won 50 percent (41 of 82) of her receiving points against Townsend's serve.
Andreescu will now meet 23rd-seeded Belgian Elise Mertens, who easily defeated American Kristie Ahn, world No. 141, to qualify for her first US Open quarterfinal in four appearances.
In other women's matches, Switzerland's Belinda Bencic pulled off one of the biggest upsets of the tournament, knocking out defending champion and world no. 1 Naomi Osaka in straight sets 7-5, 6-4.
Bencic will face Croatia's Donna Vekic, seeded 24th, who beat 26th-seeded Julia Georges of Germany, 6-7 (5), 7-5, 6-3.
The other two quarterfinals will be played between Ukraine's Elina Svitolina, seeded fifth, and Britain's 16th-seeded Johanna Konta while Serena Williams, who is ranked 8th, will face China's Quiang Wuang, ranked 18th.
( With inputs from IANS )