The Slovakian progressed from the third stage of the tournament with a 6-3 5-7 6-2 success against American wildcard Alison Riske at Flushing Meadows on Monday.
The 30-year-old is delighted that all her hard work has paid off at the Grand Slam.
"It means a lot to me to be in another quarter-final in New York," Hantuchova said in a press conference.
"In every match, I give my heart. Maybe the tennis isn't always the best but I know I am trying my hardest every point."