Serena Williams set a new Grand Slam record of 308 victories with a win over Yaroslava Shvedova of Kazakhstan at the US Open in New York.

The world number one won 6-2 6-3 to pass Roger Federer in the all-time list of matches won at the tennis majors.

Serena Williams, 34, moves on to the quarter-finals, where she will face Romanian fifth seed Simona Halep, who beat Spain’s Carla Suarez Navarro 6-2 7-5.

“It’s a huge number,” Serena Williams said of her record 308th win.

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“I think it’s very significant actually. I definitely never thought I would be playing still. Now I don’t really see when I’m going to stop.

“I’m just enjoying these moments out here, getting to break records that I didn’t even know existed or I didn’t even know was possible.”

Simona Halep has lost seven of eight matches against Serena Williams but hopes that will at least keep the pressure off in their quarter-final.

Ana Konjuh became the first Croat to reach the women’s quarter-finals at the US Open with a shock 6-4, 6-4 win over fourth seed Agnieszka Radwanska.

The 18-year-old hit 38 winners including six aces as she avenged a second-round loss to her Polish opponent at Wimbledon.

“It’s been an incredible night,” said Ana Konjuh after she made it past the third round of a Grand Slam for the first time.

“This time I got revenge, so I’m really happy.”