Ashleigh Barty kept alive home hopes of an Australian Open champion after the women's top seed defeated Petra Kvitova in straight sets on Tuesday to set up a semi-final against American Sofia Kenin. Barty, the top seed and last remaining Australian in the tournament, survived a tough opening set to beat the Czech seventh seed 7-6, 6-2 and reach the last-four at Melbourne Park for the first time. This was revenge for the 23-year-old Barty after two-time Wimbledon champion Kvitova beat her at the same stage last year in Melbourne. Yet, the Australian is a much improved player from 12 months ago, having surged to the top of the world rankings last season and won her first Grand Slam title at the French Open. She is now the favourite to win her second major title, which would make her the first Australian woman since Chris O'Neil in 1978 win the women's title Down Under. "It's been absolutely incredible. I knew that I had to bring my best today against Petra, and that first set was crucial," Barty said. Kvitova, 29, who suffered severe injury to her left playing hand in <a href="https://www.thenational.ae/sport/tennis/petra-kvitova-fortunate-to-be-alive-after-knife-attack-in-czech-republic-home-1.211374">a knife attack at her home in 2016</a>, and Barty went toe-to-toe in a crucial seventh game of the first set. In a game stretching to nearly 10 minutes, Barty fought off five break points to hold serve at Rod Laver Arena, to roars of approval. In a tense encounter they went to the tie-break, but it was Kvitova who blinked, shanking a forehand long to give Barty the set in 69 high-quality minutes. Barty, who once gave up tennis to play professional cricket, clenched her fist. Kvitova tossed her racquet into air. Barty pulled away in the second set as Kvitova wilted in the Melbourne sun. The Australian sealed the deal with her trademark minimum fuss, booking her spot in the last four with an ace, before paying tribute to her opponent. "Petra is the perfect competitor," Barty said. "She comes out here and fights her absolute best – does everything her best that she can, and regardless whether she wins or loses she’s always got a big grin on her face walking up to the net. "She’s a lovely person and that’s what has made her so good over such an extended period. I absolutely love testing myself against her. Barty will need to beat Kenin to reach her first Australian Open final after the American 14th seed saw off the unseeded Tunisian Ons Jabeur 6-4, 6-4. "It was a tough match," said Kenin. Kenin said that holding her serve at 3-2 down in the second set, in a game that stretched to 10 minutes, was a turning point. "It was a tough moment, she was playing well. I didn't know it was 10 minutes but it felt pretty long," she said. "But after that I got my momentum and started playing better." The 78th-ranked Jabeur was the <a href="https://www.thenational.ae/sport/tennis/i-m-really-proud-ons-jabeur-the-first-arab-woman-to-reach-grand-slam-quarter-final-1.969638">first Arab woman to reach a Grand Slam quarter-final</a>.