- Venue: Flushing Meadows
- Dates: 27 August - 9 September
Coverage: Listen on BBC Radio 5 live sports extra and online; live text commentary on the day's best match
Former world number one Caroline Wozniacki's US Open campaign came to an abrupt end as she lost in straight sets to Irina-Camelia Begu.
It was a poor performance by the eighth seed, who was comfortably beaten 6-2 6-2 by the world number 96 from Romania.
Serena Williams needed just 55 minutes to dispatch fellow American Coco Vandeweghe 6-1 6-1.
eased into round two with a thumping victory over Russia's Nina Bratchikova.
The Pole wore strapping on her right shoulder but showed no signs of discomfort in a 6-1 6-1 win and will be joined in the second round by 12th seed
who beat Ukrainian qualifier Elina Svitolina.
Wozniacki's 2012 Grand Slam record
- Australian Open: Quarter-final
- French Open: Third round
- Wimbledon: First round
- US Open: First round
Another ex-world number one,
dispatched American compatriot Bethanie Mattek-Sands 6-3 6-1.
Two-time champion Williams has slipped to 46th in the world amid
her struggles with Sjogren's Syndrome
but looked in superb condition during the 62 minutes she spent on court.
Next up for the seven-time Grand Slam champion is German sixth seed Angelique Kerber, who
overwhelmed Britain's Anne Keothavong.
who played with strapping on her right knee, was the day's biggest casualty.
"I didn't play particularly well, made too many errors. It's unfortunate because it's a huge tournament, a tournament you want to play well in," said the 22-year-old, who also lost in round one at Wimbledon in June.
"It's frustrating to have some injuries, but it happens to everyone. It's just about moving on.
"After the year's finished you can evaluate, you can see what was good and wasn't so good and work from there. I still have plenty of years in me. Hopefully I can just turn it around and play even better."
had no trouble reaching the second round, where she will play Spain's Maria Jose Martinez Sanchez for a place in the last 32.
"The conditions were really crazy, but, hey, it's the US Open so you have to be ready for the worst conditions," said the reigning Wimbledon and Olympic champion.
"I was ready and, coming here as Olympic champion, I feel so great."
Earlier on Tuesday, world number two Radwanska needed just 54 minutes to book a meeting with Carla Suarez Navarro of Spain.
There was no such success for her sister, Urszula Radwanska, as she went down 6-1 6-1 to 20th seed
Ivanovic, the 2008 French Open champion from Serbia, won 6-3 6-2 and will next play unseeded Swede
a 6-4 6-2 winner over 41-year-old Japanese Kimiko Date-Krumm.
the Serbian 30th seed, beat Kateryna Bondarenko 6-1 6-2, while home favourite
progressed after a 6-3 6-4 victory over 22nd seed Francesca Schiavone of Italy.