Williams was fuming after the match, irate with good reason that chair umpire Mariana Alves had called a perfectly good backhand winner out, despite there being no call from the nearby line judge.

“She said she overruled,” said Williams, a two-time champion at the tournament.

“I said: ‘How could you overrule a line that far away? Why would you even overrule that shot? It didn’t even touch the line.”’

When the pair met in Wimbledon’s quarter-finals, Capriati won just two games and failed to do herself any justice, but this time it was a different story, with the 28-year-old rising to the occasion.

It will be a fourth visit to the semi-finals for Capriati, who has yet to go one better and feature in a final of her home Grand Slam.

“There’s no place I’d rather be, no matter how hard it can actually be,” said Capriati of the tournament.

“You feel like you want to cry out there because you want to win so bad.”

For Williams, the urge to cry was for entirely different reasons.

After having another call go against her in the final game of the match, she protested: “I know my balls were in. It wasn’t just that point, that’s the thing. I know my shots. I know in the last game those balls were in as well. So it’s like, what do you do? You just got to keep fighting.”

Capriati booked her place in the last four on her third match point.

“Just to be at this point, I’m very happy,” she remarked.

“I think I can be happy with what I’ve done and achieved. And even win or not win, I should just be thankful that I’m here. And it would be great to win, but if I don’t, life goes on.”

Alves was the focus of much of the after-match attention, and tournament referee Brian Earley later apologised for the umpire providing the defining moment of the contest.

“Regrettably, the replay on television showed that an incorrect overrule was made,” said Earley.

“A mistake was made and I have discussed the call with Ms Alves. Ms Alves is not scheduled to officiate another match during the 2004 US Open.”

Standing between Capriati and a place in the final, where she would be seeking a fourth career Grand Slam title, is Russia’s Elena Dementieva.

In Capriati’s favour is a record of three wins in three matches against Dementieva.

Dementieva, however, can point to her quarter-final victory over France’s second seed Amelie Mauresmo as proof of her fine form this fortnight.

The sixth-seeded Russian could barely stand come the end of the match, which was as dramatic as it was often disappointing in standard, but outlasted Mauresmo 4-6 6-4 7-6 (7/1).

The match featured 14 breaks of serve in 33 games, with Dementieva having to battle her way back into the decisive set after falling 4-3 – with a break in Mauresmo’s favour – behind.

Mauresmo could yet find consolation, however, because she will displace Justine Henin-Hardenne as world number one unless Lindsay Davenport collects the title this weekend.

“I think when you reach that number one spot, it’s great. But I would have loved to do it in a good way,” said the Parisian.

Each of the four men’s fourth-round matches were won in straight sets, with Andy Roddick and Lleyton Hewitt among those bullying their way into the last eight.

Australian Hewitt looked ominously good as he posted his fourth consecutive straight-sets victory, routing Karol Beck of Slovakia 6-4 6-2 6-2.

He has now won 14 consecutive matches, having triumphed in his two tournaments preceding Flushing Meadows, but may be stiffly tested by back-to-form German Tommy Haas in the quarter-finals.

Haas beat 18-year-old Czech Tomas Berdych – the teenager who ousted Roger Federer at the Olympics – 7-6 (8/6) 6-1 7-5.

American Roddick delighted the late-night crowd, who had been enthralled by the Capriati-Williams duel, by making further smooth progress at the tournament where he is defending champion.

A 6-3 6-2 6-4 victory over 18th-seeded Spaniard Tommy Robredo was exactly what Roddick was seeking. Ruthless, efficient, and all over in barely an hour and a half.

Joachim Johansson of Sweden, seeded 28th, is the next in line for Roddick, who blasted one 149mph serve past an outclassed Robredo.

Johansson eased to a 6-2 6-3 6-2 victory over France’s Michael Llodra.