Venus Williams during her match against Jelena Jankovic in New York on Wednesday. (AP)

Jelena Jankovic laughed at herself stretching into splits, smiled in wonder at Venus Williams’s wingspan and was star-struck when she saw the comedian Jerry Seinfeld applaud her play on the big New York stage.

Jankovic had already played two three-setters in earlier rounds of the Open. She was determined to have fun in her quarter final under the lights at the Arthur Ashe Stadium.

Venus, locked in a business meeting with herself all night, was having none of it.

Not until she sent Jankovic out the door Thursday night, with a shriek and a monstrous swinging forehand volley winner in the dramatic third set tie-breaker, could Venus break into a wide grin.

Charging to the net all night, Venus attacked for a 4-6, 6-1, 7-6 (7-4) victory, advancing to the semis here for the first time since 2002. She will now play No. 1 Justine Henin, who dismantled Venus’s younger sister Serena in the quarter final the night before.

“I wasn’t happy with the result at all, to say the very least,” Venus said of her sister’s defeat. “I was sad that Serena lost. I didn’t like to see her so upset. I definitely will have to win for Williams.”

Unlike Serena’s loss to Henin, which ended with the former’s sour lack of respect for her opponent, this match held both sizzle and sportsmanship, delivering as promised.

Of course, Jankovic did not like the promises she had heard over the past two days.

“I was listening to the commentators,” she said. “I was so sure that Venus was the favourite. They kept going, Venus will play Justine. Venus will do this. They already put me out, and I’d beaten her the last three times.”

Later, she had to laugh. “I guess they were right,” she said.

Venus and Henin have not played since the semis of the Australian Open in 2003, before Henin won her six Grand Slam titles. Henin won their first meeting, on clay in Berlin in 2001, and since then the American has won seven matches in a row.

Venus was back at her hotel watching her sister’s match on Tuesday and had this assessment of what Henin must do to beat her: “Serena and I, we play different, even though we’re both very powerful. So I think she’ll definitely, obviously have to play well. Quite obviously, I’ll have to play well, too.”

At 27, Venus, who won Wimbledon for her sixth Grand Slam title, appears to be playing better than ever, despite her lack of match play this season.

Jankovic, from Serbia by way of Nick Bollettieri’s academy in Florida, has been the road warrior of women’s tennis this season. She had played in 22 tournaments and 82 matches this season, while Venus floated into only 10 tournaments, playing 44 matches.

By the end, it was clear: No one covers more ground than Venus. Jankovic conceded that if Venus’s reach and powerful serve did not overwhelm her, then the aggregate effect of all that tennis caught up with her in this match.

“I think it’s nice to be fair, to give credit to the opponent,” Jankovic said. “When she hits a great shot, why not? There’s nothing wrong with smiling on the court.”