NEW YORK (AFP) - Second-ranked Jelena Jankovic moved closer to her first Grand Slam title and reclaiming the world number one ranking with a 3-6, 6-2, 6-1 triumph Sunday over Denmark's Caroline Wozniacki at the US Open. The 23-year-old Serbian advanced to the quarter-finals of the year's last major tennis tournament, rallying in blustery conditions at Arthur Ashe Stadium to defeat an 18-year-old who won August WTA titles at Stockholm and New Haven. "In the first set she played quite solid. I was the one who was all over the place. I couldn't find my rhythm in these conditions and she took advantage of that," Jankovic said. "I stayed calm and composed and knew I had to do something to change that. In the second set I did the smart things and I cruised through the second and third set." Jankovic, who spent a week as world number one earlier in August, will next face Austrian Sybille Bammer, whom she has beaten in six of seven meetings, most recently in the fourth round of last year's US Open. Defeating Bammer again would ensure Jankovic a chance to reclaim the top spot although Serena Williams, Elena Dementieva, Dinara Safina also remain in the mix to be number one after the Flushing Meadows fortnight. "It would be nice to come back to the number one spot," Jankovic said. "It would be great if I can do it. We will see what happens." With top seed Ana Ivanovic of Serbia and Russian third seed Svetlana Kuznetsova already ousted, this is a prime chance for a Slam breakthrough. "I want to win a Grand Slam," Jankovic said. "By winning a Grand Slam I would regain the number one ranking again. It's something I want to achieve again." Jankovic reached the French and Australian Open semi-finals but was upset in the fourth round at Wimbledon by Thailand's Tamarine Tanasugarn after hurting her knee in a third-round victory over Wozniacki. "I have been injured. Right now I finally do not have any problems," Jankovic said. "Little by little I feel like I'm getting better every day. "I feel the shots a lot better than I did at the beginning of the tournament. That's my goal, get my game together by the end of the tournament." Jankovic was down a set and in a fight during the second before cracking the Danish teen on her third break-point chance of the sixth game for a 4-2 edge. "I started well. I played aggressive," Wozniacki said. "The second set, I got a bit more defensive. Even though I was hitting the ball, it wasn't going well. She kept coming in and forcing play. She was just better than me." Jankovic, who also lost the first set to Wozniacki this year at Wimbledon, broke again to finish the second set and again in the fourth and sixth games of the third set to secure the triumph. "I'm getting better each day. I'm improving on my fitness," Jankovic said. "I can push off better. Little by little I'm putting the pieces together. I'm bringing my game to the next level. I believe in myself." Olympic champion Dementieva, who can take the top spot if she reaches her first Grand Slam final since the 2004 US Open, defeated China's Li Na 6-4, 6-1 in just 61 minutes. "This is a dream for me, to become number one, but I'm not thinking about it. I want to focus on this tournament," Dementieva said. "I don't want to put all this pressure on myself." The Russian fifth seed booked a quarter-final date against Swiss 15th seed Patty Schnyder, who rallied to defeat Slovenia's Katarina Srebotnik 4-6, 6-3, 6-3. Dementieva says she is rounding her game into top form after the Olympics. "I played very well in Beijing," she said. "Because of the recovery I don't think I'm playing at my best but I am slowly improving and I hopefully will play better in the next match." Bammer ousted French 12th seed Marion Bartoli 7-6 (7/3), 0-6, 6-4 with Bartoli weakened by a sick stomach and defying doctor's advice not to play because of low blood pressure. "It's a miracle I could manage three sets," Bartoli said.