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The 19-year-old Serbian was broken in the first game of the match as Rezai succeeded in catching her cold, and when the Frenchwoman sent an ace straight down the middle to move 3-1 up, it seemed an upset could be on the cards.

Ivanovic was stung into action, and immediately went on the offensive herself, sending frequent winners past her opponent as she reeled off five games in a row to take the first set 6-3.

She kept the form into the second set, only stuttering at 3-0 when she surrendered her serve with an overhit pass.

Undeterred, Ivanovic broke Rezai twice more to wrap up victory and set up a third round clash with Russian Vera Dushevina, who beat compatriot Ekaterina Bychkova 6-4 6-3.

American Venus Williams also moved into the third round with a 6-4 6-2 win over Romanian Ioana Olaru.

The Wimbledon champion is scheduled to meet the French Open finalist Ivanovic in the fourth round if both women win their next matches.

The 12th seeded Venus looked set to dominate the match after racing into a 3-0, her play sprinkled with flamboyant drive-volleys and athletic overheads.

She then ran into commendable resistance from Olaru, who broke back at 5-4, only for the American to again go on the attack and return the favour to claim the first set.

Though she struggled to get to grips with the power of the Williams serve, Olaru steadfastly refused to surrender her own serve, and was only broken when the American sent a rasping forehand crosscourt winner past her to move 4-2 ahead.

From that point there was no looking back as she cut through the final two games swiftly to book a third-round meeting with either Eleni Daniilidou or Alyona Bondarenko.

There was a minor second-round surprise when Japan's 28th seed Ai Sugiyama (28) fell to Russian Ekaterina Makarova 6-4 4-6 6-2.

Also in action on Tuesday are Serena and Venus Williams, top seed Justine Henin, and third seed Jelena Jankovic.

Follow LIVE coverage of the entire US Open on eurosport.yahoo.com.

Michael Fitzgerald / Eurosport