MELBOURNE (AFP) - Third seed Dinara Safina survived two match points against France's Alize Cornet to claw her way into the quarter-finals of the Australian Open with a 6-2, 2-6, 7-5 win on Sunday. The Russian appeared certain to follow Jelena Jankovic, Venus Williams and Ana Ivanovic out of the tournament when Cornet was serving for the match at 5-4 and 40-15, but she somehow clung in there and dug herself out of trouble. Three games later Safina was raising her arms in triumph as Cornet was slumped in a chair in tears, her dreams of joining fellow Frenchwoman Marion Bartoli in the quarter-finals in tatters. "I feel so lucky that I have the chance to play in the quarter-finals," Safina said. "I think in the next round I need to relax for me and my team - I think they nearly had heart attacks watching me." There was no indication of the drama that was to follow as Safina cruised through the first set and completely dominated her opponent, hitting winner after winner and forcing Cornet into errors. Cornet didn't win her first game until 0-5 in the first set when she surprisingly broke Safina's serve, then held her own to get to 2-5. Safina broke Cornet again to take the first set in 29 minutes then comfortably held her own at the start of the second and a passage to the quarter-finals looked assured. However, Cornet came storming back as Safina's unforced error rate skyrocketed and she won the next five games, eventually taking the set 6-2 to head into the decider with her confidence high. Safina held her first game, as did Cornet, but the Russian then served a loose service game to go behind a break. Just when it looked like Safina was gone, she broke Cornet to love to get back on track. But incredibly she surrendered the break the next game, missing three easy shots to an open court. Safina had another chance for yet another break in the next game when she had Cornet at 15-40 but played a series of loose shots and Cornet moved to a 4-2 lead. With the mistakes continuing to fly off Safina's racquet, Cornet broke again to find herself 5-2 and serving for the match. But Safina dug deep and broke back, then served a solid game to get to 4-5. Cornet answered the challenge and had two match points at 40-15 but Safina suddenly couldn't miss and she overpowered her opponent to get the break and move to 5-5. She then served well to hit the lead in the decider for the first time since the opening game. Cornet came out to serve to stay in the match and although she got to 40-30 she couldn't close it out. The Russian then brought up a match point, which Cornet saved, but she then brought up a second and there was no coming back for the Frenchwoman.