American sixth seed Williams battled back from one-set down to take her place in the last eight.

Kournikova started well and confounded Williams when she cleverly mixed her tactics.

But 19-year-old Williams got her power game going in the second set and had the 18-year-old Russian chasing all over the court.

Kournikova comes to terms with her collapse on court 18

Williams won 3-6 6-3 6-2 in one hour, 32 minutes and will face six-time champion Steffi Graf for a place in the semi-finals.

Williams admitted she had struggled at first: "I was just not able to get started. I was making mistakes and she was hitting some good shots.

"I knew I had to do better in the second set otherwise I would be booking a flight home.

"I now play Steffi Graf and I have beaten her the last two times we played. I'll go out there ready to play and ready to attack."

Steffi strolls

Graf took just eight minutes to book her place in the quarter-finals at the expense of qualifier Kim Clijsters.

Steffi Graf explains how much more she is appreciating her success

The match was stopped by rain on Monday with the German leading 6-2 4-2 and she started where she had left off.

Graf held serve and then converted her fourth match point on the Clijsters serve to take the second set 6-2.

Second seed Graf, aged 30, reached her 10th singles quarter-final at SW19 _ and she has only ever lost once at that stage of the tournament.

Stevenson wrecks Raymond's bid

Wimbledon debutant Alexandra Stevenson continued her impressive march through the tournament as she hit back to beat Lisa Raymond and reach the last eight.

The 18-year-old American only won one point in the first four games and lost the first set for the first time this tournament but stayed calm.

She hit back to win the second on a tie-break and took command after that.

Stevenson broke Raymond twice in the final set to complete an impressive 2-6 7-6 (10-8) 6-1 victory.

Tauziat triumphs

Last year's finalist Nathalie Tauziat beat Dominique van Roost of Belgium 6-3 3-6 6-3.

In a tight match there was only break of serve in the first two sets, with Tauziat managing two to Van Roost's one in the decider.

Croatian 17-year-old Mirjana Lucic reached her first-ever Grand Slam quarter-final with a straight sets win over Tamarine Tanasugarn of Thailand.