Hantuchova won 6-3 5-7 6-2 after repelling a fightback from Riske, who upset 2011 Wimbledon champion Petra Kvitova to reach the fourth round at a grand slam for the first time.
Hantuchova was just 19 when she made the last eight at Flushing Meadows in 2002 but had not been back to the quarter-finals since.
The 30-year-old seemed to be cruising to victory against Riske after she raced through the opening set in just 37 minutes then led 4-2 in the second.
But the American, seven years younger, broke back to level the second set at 4-4 when the match was stopped for nearly five hours because of a thunderstorm.
When play resumed, Riske pounced, winning the set and forcing a deciding third, but could no hold off Hantuchova, who saved four points in her third round clash with Julia Glushko to continue.
"It means a lot to me to be in another quarter-final in New York," said Hantuchova.
"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."
Hantuchova is one of just two unseeded players left in the women's singles draw. Her next opponent will be either world number two Victoria Azarenka or former world number one Ana Ivanovic.
Their fourth round match was postponed until Tuesday because of the inclement weather.
(Reporting by Julian Linden,; editing by Gene Cherry)
