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Serena Williams flirted with grand slam danger once again but kept her calendar-year Grand Slam bid on track by beating a battling, 101st-ranked Bethanie Mattek-Sands 3-6 7-5 6-0 at the US Open.

Williams, who lost nine sets, including seven first-set losses, in her charge to the Australian, French and Wimbledon titles this year, was tested at Flushing Meadows by her fellow American, but roared back to victory to reach the fourth round.

"I'm not trying to live on the edge," the 33-year-old Williams said in an on-court interview.

"I'm playing players that come out really strong. I just think Bethanie played really well.

The 21-times grand slam singles winner, who is aiming to join Maureen Connolly (1953), Margaret Court (1970) and Steffi Graf (1988) as the only women to sweep the four grand slams in a single season, next faces fellow American Madison Keys.

Keys advanced 6-3 6-2 over 15th seed Agnieszka Radwanska of Poland.

Venus Williams, who won the second of her two US Open titles 14 years ago, beat Swiss teen Belinda Bencic 6-3 6-4.

Venus, 35, produced a vintage power-game performance to beat the 18-year-old in a match-up between the oldest and youngest players left in the women's draw.

Venus vs Bencic was a match-up between the oldest and youngest players left in the women's draw [AP]

"I just wanted to stay aggressive and keep my errors down," said Venus, who had also beaten Bencic in straight sets in their three previous encounters.

Joining the seven-times grand slam singles winner in the fourth round was Russian 13th seed Ekaterina Makarova, who advanced with 6-3 7-5 victory over 17th seed Elina Svitolina of Ukraine.

Results:

1-Serena Williams (U.S.) beat Bethanie Mattek-Sands (U.S.) 3-6 7-5 6-0
Anett Kontaveit (Estonia) beat Madison Brengle (U.S.) 6-2 3-6 6-0
Roberta Vinci (Italy) beat Mariana Duque (Colombia) 6-1 5-7 6-2
23-Venus Williams (U.S.) beat 12-Belinda Bencic (Switzerland) 6-3 6-4
13-Ekaterina Makarova (Russia) beat 17-Elina Svitolina (Ukraine) 6-3 7-5
Kristina Mladenovic (France) beat Darya Kasatkina (Russia) 6-2 6-3
19-Madison Keys (U.S.) beat 15-Agnieszka Radwanska (Poland) 6-3 6-2
25-Eugenie Bouchard (Canada) beat Dominika Cibulkova (Slovakia) 7-6(9) 4-6 6-3

Source: Reuters