You never quite know when Serena Williams is being serious or joking around, but when she raised her arms in celebration yesterday and said "I finally made a quarter-final this year", there seemed to be more than an element of relief in her voice.

The world No.1 and two-time defending champion beat Kaia Kanepi of Estonia 6-3, 6-3 to reach the last eight, the first time she has made it that far in the four grand slams in 2014.

No one has managed more than three games in a set against the American so far here this year and she will be confident of seeing off another 32-year-old, Flavia Pennetta, in the quarter-finals. But the way she dropped serve tamely when trying to close it out at 5-2 in the second set suggests an element of stress.

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"I think I felt it in my serving game [at 5-2]," she said. "I was just, like, please can I make it to the quarters of a slam this year?

"[Kanepi] plays really well, hits the ball incredibly hard and she's able to move the ball around really well. I just relaxed and said 'Serena, whatever happens, you're still in doubles'."

Williams and Pennetta will be sharing 64 years when they step out to face each other in the quarter-finals tomorrow. And although the American has won all five of their previous meetings, she knows better than to expect anything other than a tough match against the 11th seed, who beat Australia's Casey Dellacqua 7-5, 6-2 yesterday.

"Flavia's such a great mover and plays really well," Williams said. "We played each other not so long ago but she does everything well. I am just trying to enjoy everything out here and stay relaxed."

Pennetta continued her love affair with New York as she reached the quarter-finals for the fifth time in seven years, showing off her full range of shots, including some feather-light drop shots.

Pennetta, who is also playing doubles with Martina Hingis here, could not put her finger on why she plays so well in New York, compared to the other three grand slams, where she has made the quarter-finals just once.

"There is something, I don't know," she said. "I like the city all the time. When I get to New York, I feel much better. In New Haven I wasn't playing really well but as soon as I came here I was already more happy."

Pennetta said she would not try to do anything different to prepare for her sixth meeting with Williams, despite their head-to-head record.

"You cannot invent something," she said. "Of course, she's better than me, but if I still believe I can beat her, maybe if she doesn't have a good day, I can do that. If I go on court and just play and try not to lose 6-0, 6-0, I am going to lose 6-0, 6-0."