(CNN) -- The last time Svetlana Kuznetsova beat Serena Williams, the Russian went on to win the French Open.
When they meet again this week, that 2009 quarterfinal clash will be on both their minds.
"It will be a good match -- I mean, the last time we played here, she won," Williams said after reaching the last eight at Roland Garros with Sunday's comprehensive 6-1 6-3 victory over Italian clay specialist Roberta Vinci.
"That will probably get her pumped up, and she's on a comeback, and she has nothing to lose and everything to gain. She's also won this tournament before.
"So it's not going to be an easy match for me, for sure. But I don't want to stop at the quarters."
Williams lost in the first round in Paris last year, but has dominated the women's game since then -- winning Wimbledon, the Olympic singles and doubles, the U.S. Open and the WTA Championships.
The American surprisingly lost in the Australian Open quarterfinals in January, but is now on a 28-match winning streak as she seeks to follow up her only French success back in 2002.
That run has only been surpassed this decade by her older sister Venus (35 wins) and Justine Henin (32).
"I honestly don't even consider it a streak," Williams said. "Every day, everybody's like, 'You're on this streak.' But for me it's about winning the matches.
"It's like I don't care to be on a streak; I don't care not to be on a streak. I just want to win this match. If that means it's going to be consecutive and it's going to be winning streaks, that's great.
"But at the end of the day, I just want to hold up the winner's trophy and whatever it takes to get there."
Williams has won 15 grand slam titles, and Kuznetsova is seeking her third as she rebuilds her career after injury problems that meant she has had to play qualifying events to get into the main draw of some of the bigger tournaments this year.
"I am excited to come back, it's been six months off," the 27-year-old told CNN's Open Court before the French Open.
"It was my biggest break for my whole career and I was a little bit tired -- nonstop for 12 years all the time from January to November every year."
Kuznetsova, like Williams, reached the quarterfinals in Melbourne and has matched that in Paris after beating German eighth seed Angelique Kerber 6-4 4-6 6-3 on Sunday.
She has won only two of eight encounters with Williams, the other being in Stuttgart in 2007 -- a year in which she reached the final of the U.S. Open but could not match her 2004 success in New York.
"I'll just go out there and play my game," the world No. 39 told reporters. "Sometimes I can be very good. Sometimes I just have bad days.
"I'm just a human being, maybe even more than other people. But I'm just trying to do my job.
"I don't care if I'm an underdog or not, I just go out there and try to play my game."
Last year's runner-up Sara Errani also reached the quarterfinals, with the Italian fifth seed battling to a 5-7 6-4 6-3 win over Spain's Carla Suarez Navarro.
Errani, who makes up the top-ranked doubles team with compatriot Vinci, needed two and a half hours on court before beating the world No. 20 -- who was hoping to match her last-eight appearance in Paris in 2008.
Errani will next play Polish world No. 4 Agnieszka Radwanska, who won 6-2 6-4 against 2008 champion Ana Ivanovic of Serbia.