Jankoviv had to dig deep to see off Arvidsson in the third set

World number two Jelena Jankovic was pushed all the way by Sofia Arvidsson before winning 6-3 6-7 (5-7) 6-4 to reach the third round of the US Open.

Both players had chances in a marathon third set before an exhausted Jankovic triumphed in two hours and 44 minutes.

Third seed Svetlana Kuznetsova and fifth seed Elena Dementieva also won but eighth seed Vera Zvonareva lost 6-3 6-3 to Ukrainian Tatiana Perebiynis.

Lindsay Davenport beat Alisa Kleybanova 7-5 6-3 in the night match.

The 1998 champion was repeatedly pegged back by the Russian teenager in a scrappy match but eventually prevailed in one hour 31 minutes.

It was really tough - I am completely out of breath Jelena Jankovic

"I didn't play quite as well as I did (in the first round)," said the American, 32. "Didn't find my rhythm but sometimes you just have to get through these matches."

Kuznetsova, the 2004 champion and last year's runner-up, was given an early scare before beating Romania's Sorana Cirstea 7-6 (7-3) 6-1.

The Russian trailed 4-2 in the first set but recovered to level at 4-4 and went on to take it on a tie-break.

Cirstea's game fell away badly after that and Kuznetsova eased to victory.

"In the first set I went out there but I had no clue how she would play," said Kuznetsova.

"She plays the ball really flat and fast so, for me, it was all about the first set. I realised I had to go more to the forehand because (on her) backhand she was making good shots."

Fifth seed Dementieva, the Olympic champion, thumped France's France's Pauline Parmentier 6-2 6-1.

Dementieva will play British number one Anne Keothavong in the last 32.

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Jankovic

, who is seeded second, served for the match in the second set and also opened up a 3-0 lead in the tie-break but Arvidsson did not give up.

The world number 63, who lost another epic encounter with Jankovic in Miami earlier in 2008, trailed 3-0 in the decider but broke back to level at 4-4 before Jankovic made a final push for victory.

"It was really tough," Jankovic said. "I am completely out of breath. I was pushed to the limit.

"The last time I played her, she was 5-1 up in the third set and I had to come back."

And the Serbian later revealed that she had to stop her post-match run on the treadmill when pain flared in the area of a knee injury sustained at Wimbledon.

"I couldn't go any more," said Jankovic. "My leg was straight and I couldn't bend it. The muscle was in spasm and I had a lot of pain."

Jankovic faces Wimbledon semi-finalist Jie Zheng next after she beat Anabel Medina Garrigues 6-1 6-4.

Swiss 15th seed Patty Schnyder made it through, beating Anastasia Pavlyuchenkova of Russia 6-3 6-3.

There were also straight-sets wins for 12th seed Marion Bartoli, 14th seed Victoria Azarenka and 21st seed Caroline Wozniacki.

But Zvonareva, who won a bronze medal in Beijing, tumbled to a straight-sets defeat against Perebiynis, the world number 76.

Jankovic, Kuznetsova, Dementieva, Serena Williams, and Dinara Safina all have a mathematical chance of becoming world number one if any of them reach the final.

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