Romanian second seed Simona Halep followed the same express path into the second round of the US Open as Serena Williams, advancing 6-2 3-0 after New Zealand's Marina Erakovic retired with a knee injury on Tuesday.

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The in-form Halep, who reached the finals at US Open tune-up events in Toronto and Cincinnati, barely broke a sweat on a sunny Arthur Ashe Stadium court, needing a mere 47 minutes to see off the 99th ranked New Zealander.

Top seed Williams, bidding to complete a calendar sweep of the four grand slams, advanced on Monday in similar fashion as she was up 6-0 2-0 when Russia's Vitalia Diatchenko was forced to retire hurt.

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While the top two women's seeds steered clear of trouble, upsets continued up and down the women's draw for a second consecutive day as sixth seed and French Open finalist Lucie Safarova fell 6-4 6-1 to Ukrainian Lesia Tsurenko.

With the loss, Safarova joins a number of first round casualties that already includes Serbian seventh seed Ana Ivanovic, eighth seeded Czech Karolina Pliskova and 10th-seed Carla Suarez Navarro of Spain.

"I wasn't surprised (by the upsets), it is normal," said 23-year-old Halep. "Everyone is fighting like crazy because it's the last grand slam (of the year). When you play the grand slam you have just to give everything you have. I had this year already two grand slams where I lost in first and the second round, so like I say always, everything can happen."