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(Adds later results)
* Williams powers past Cibulkova
* Gritty Sharapova beats Kanepi
By Ciaran Baynes
BRISBANE, Jan 2 (Reuters) - Maria Sharapova rallied to beat Kaia Kanepi on Thursday and next faces Serena Williams in the Brisbane International semi-finals knowing she must dramatically improve to end a run of 13 straight defeats against her nemesis.
World number one Williams comfortably ousted Slovakian Dominika Cibulkova 6-3 6-3 in 61 minutes, winning the first set without losing a point on serve - a feat the American had not achieved since she was a junior.
Sharapova was involved in an error-strewn battle, coming from a set down to defeat Estonia's Kanepi 4-6 6-3 6-2 in two hours.
The pattern was set at the start as the match began with four successive breaks of serve.
Had 2012 champion Kanepi been in better form, the Sharapova-Williams showdown that the tournament organisers hoped for would have been scuppered.
The Russian improved as the match went on and in the third set her service accuracy improved to 84 percent, nearly double her efforts in the first two sets.
"You're going up against a great champion that's playing great tennis at the moment," Sharapova told reporters of her clash with Williams. "You know that you have to raise your level in order to beat her.
"I think the intensity level of our matches are always high. I think she goes up and wants to play the best tennis against me."
When asked about her frosty off-court relationship with Williams, the Russian replied: "I have said everything I have to say about it".
The American played down the animosity between the pair, saying: "I don't have anything against her".
Elsewhere, second seed Victoria Azarenka let slip nine match points before finally beating Stefanie Voegele of Switzerland 6-4 6-7 (7-9) 6-1.
The Belarusian next plays fourth-seeded Serb Jelena Jankovic who defeated German Angelique Kerber 6-7 (8-10) 6-3 6-1.
In the men's event, unseeded Australian Lleyton Hewitt beat sixth-seeded Spaniard Feliciano Lopez 7-5 6-3 and next faces Romanian qualifier Marius Copil in the quarter-finals.
Copil put out third seed Gilles Simon of France 7-5 6-3. (Editing by Tony Jimenez)