NEW YORK — Venus Williams went from down and out to a point from victory, then back again. In the end, she couldn’t quite get past a woman a dozen years younger and never before at this stage of a Grand Slam tournament.

Williams failed to convert a match point and lost 4-6, 6-4, 7-6 (3) to 10th-seeded Karolina Pliskova of the Czech Republic in the fourth round of the U.S. Open on Monday, despite vociferous support from the Arthur Ashe Stadium crowd down the stretch.

“I really played the perfect point there,” the sixth-seeded Williams said about her chance to end things while up 5-4 in the third set, and Pliskova serving at 30-40, “and she managed to stay alive.”

At 36, Williams would have been the oldest woman to reach the quarterfinals at any major since Martina Navratilova was 37 at Wimbledon in 1994.

Williams made it that far at Flushing Meadows a year ago, before losing to her younger sister Serena. This time, they had been on course for an all-in-the-family showdown in the semifinals; Serena followed Venus in Ashe and beat Yaroslava Shvedova 6-2, 6-3 in the fourth round for her 308th Grand Slam match victory, breaking a tie with Roger Federer for most in the Open era, which dates to 1968.

Pliskova managed to make it to her first Grand Slam quarterfinal at age 24.