Tennis: Serena Williams sets new slam mark

Serena Williams, of the United States, returns a shot to Johanna Larsson, of Sweden, during the third round of the U.S. Open. Photo / AP.

Another win, another milestone for Serena Williams who rolled into the last-16 of the US Open by crushing Sweden's Johanna Larsson 6-2 6-1 to collect grand slam victory number 307 - the most by a woman in the Open era.

As in the majority of her victories at the majors, Williams operated with ruthless efficiency but displayed little fire as she coolly dispatched the 47th-ranked Swede in exactly one hour.

The victory moved the 34-year-old American past Martina Navratilova and level with Roger Federer for most grand slam victories by a man or woman.

Williams will go for number 308 and a step closer to what would be a record seventh US Open title when she meets Kazakhstan's Yaroslava Shvedova, a 6-2 7-5 winner over China's Zhang Shuai, in round four.

Agnieszka Radwanska registered an unusually comfortable third-round win over France's Caroline Garcia.

Radwanska, who had been extended to three sets in three of her four matches against 25th seed Garcia, romped into the round of 16 with a 6-2 6-3 victory in breezy conditions at Louis Armstrong Stadium.

It will be the 27-year-old Radwanska's fifth trip to the fourth round at the US Open but she has failed to advance beyond that stage in New York.

"That means everything," Radwanska said.

"I hope I can play even better than today in the next round and reach my first quarter-final here."

Standing in her way to an elusive berth in the quarters will be either American Varvara Lepchenko or Ana Konjuh of Croatia, both unseeded.

Fifth-seeded Belgian Simona Halep narrowly avoided a third-round upset with a 6-1 2-6 6-4 win over Hungary's Timea Babos to keep her US Open title hopes alive.

Halep came into the match having dropped nine games in her opening two matches and looked ready to make speedy work of Babos but she needed two hours and eight minutes on an overcast Arthur Ashe Stadium.

Next up for Halep is 11th-seeded Spaniard Carla Suarez Navarro who advanced with a tidy 6-4 6-3 win over Russian Elena Vesnina.