PARIS (Reuters) - World number one Martina Hingis moved closer to a first French Open title Sunday, beating Romania's Ruxandra Dragomir 6-3 7-6 and hearing the welcome news that her quarter-final opponent would not be Venus Williams.

The Swiss was delighted to learn that fifth-seeded American Williams had fallen to Austrian qualifier Barbara Schwartz.

Since the draw for the French Open was made 10 days ago, the prospect of a quarter-final clash between Hingis and Williams had hung in the air tantalisingly.

But the 20-year-old Schwartz upset the formbook when she finessed her way past the hard-hitting Williams 2-6 7-6 6-3.

``Of course I'm happy with the result, now I don't have to play Venus again,'' admitted Hingis. ``It's always good to know you don't have to play a player you don't like to play.''

On the other side of the draw, second seed Lindsay Davenport kept pace with her Swiss rival, advancing with a tidy 6-2 6-3 win over American compatriot Jennifer Capriati.

Five-times French champion Steffi Graf continued to prove she has legitimate title pretensions as she disposed of Russian teenager Anna Kournikova 6-3 7-6.

With a 10-match winning streak behind her and not a single set dropped in her first three matches in Paris, Williams looked certain to blow Schwartz off court as she raced through the opening set of their match on the Suzanne Lenglen court.

Despite a few awkward moments in the second, the 18-year-old American was soon in position to walk off the court a straight sets winner.

But a jittery Williams was unable to convert any of three match points when Schwartz was serving at 5-6 in the second.

The Austrian eventually forced the set to a tie-break which she won 9-7.

Schwartz recorded the decisive break at 5-3 in the third set and then held serve for the match, but not before showing signs of nerves herself, squandering two match points before finishing the American off with a blistering backhand winner.

``I had three match points but she played some great shots,'' conceded Williams. ``She played well. It's a good win for her, I quess a good win for Austria.

``Usually when I lose a match, I really beat myself. But this time I really think she came out and played.''

Williams and younger sister Serena were seen as the two biggest obstacles between Hingis and a place in next Saturday's final but now both have been removed.

Serena was knocked out in the third round by fellow American Mary Joe Fernandez.

Fernandez, however, pulled out of the tournament Sunday with a thigh injury, handing a walkover into the final eight for defending champion Arantxa Sanchez-Vicario, the seventh seed.

After struggling to get past 16-year-old Belgian Justine Henin and unknown Colombian Fabiola Zuluaga, Davenport produced her easiest win of the first week, needing just 62 minutes to dispose of a rejuvenated Capriati.

Capriati, who appears to have finally put her troubled past behind her, ran into big problems on the court as Davenport used her superior power to lethal effect.

In a battle of unseeded Spaniards, Conchita Martinez, three times a semifinalist in Paris, made it through to the final eight speeding past Gala Leon Garcia 6-2 6-1.