Former world number one Jelena Jankovic struggled into the US Open's second round on Tuesday while Chinese eighth seed Li Na became the first major upset victim at the year's last Grand Slam event. Fourth-seeded Serbian Jankovic, seeking her first Grand Slam title, beat 96th- rated Romanian teen Simona Halep 6-4, 4-6, 7-5. The 2008 US Open runner-up nearly suffered her first opening-match Slam exit since the 2005 French Open. 'For me, first match is always the toughest. She played really well,' said Jankovic. 'I had to work for every point. I wasn't playing my best tennis. I was able to find a way to get through.' Jankovic, whose only Grand Slam final was her 2008 US Open loss to Serena Williams, and Danish top seed Caroline Wozniacki can move past injured Williams to claim the world number one spot by capturing the US Open title. Wozniacki, who lost to Kim Clijsters in last year's US Open final, begins her title quest Tuesday night against US wild card Chelsey Gullickson. Li, the highest Chinese seed in Grand Slam history, lost 2-6, 6-4, 6-2 to Ukraine's Kateryna Bondarenko. The Australian Open semi-finalist had not lost a Grand Slam opener since the 2006 Australian Open. 'It was sad to lose in the first round,' Li said. 'I just have to forget everything and practice again and hope I come back again soon.' Li breezed through the first set in 31 minutes but wilted in the afternoon heat while Bondarenko, ranked 59th, showed the form that made her a US Open quarter- finalist last year for her best career Grand Slam showing. 'It was so hot,' Li said. 'I felt good in the first set. The second set, I felt like I died. The energy just faded.' Russian seventh seed Vera Zvonareva, the Wimbledon runner-up, advanced by defeating Slovakia's Zuzana Kucova 6-2, 6-1 while Russian 11th seed Svetlana Kuznetsova beat Japan's Kimiko Date Krumm 6-2, 4-6, 6-1. And Russian 14th seed Maria Sharapova, a three-time Grand Slam champion on a path to face Wozniacki in the fourth round, made a solid start by outlasting Australia's 60th-ranked Jarmila Groth 4-6, 6-3, 6-1. 'I knew I had a tough first-round opponent,' Sharapova said. 'She came out firing and didn't give me many opportunities. These are the types of matches you want to get through to try and get better.' Jankovic, 1-3 in US Open tuneups, won her only 2010 title in March on the Indian Wells hardcourts, where she beat Wozniacki in the final. But Jankovic still has faith she has what it takes to win a Grand Slam crown. 'I know I can do that,' Jankovic said. 'It's just a matter of believing in myself, having the confidence and doing the right things on the court because I really want to get my tennis to another level.' Jankovic advanced despite 48 unforced errors. 'I made a lot of errors. I just tried to move on and play the best I could,' Jankovic said. 'You just have to fight and try your best, give your maximum and get through. It gives you a lot more confidence for the next round.' Jankovic will play 150th-ranked Croatian qualifier Mirjana Lucic in the second round. Lucic, a 1999 Wimbledon semi-finalist, ousted Australian Alicia Molik 7-6 (7/5), 6-1 for her first Grand Slam victory since the 2002 French Open as she attempts a comeback at age 28 after missing four full seasons. 'I feel fantastic,' Lucic said. 'I'm so happy. I worked so hard to get here. It's my first US Open in eight years. Feels incredible. It just feels so rewarding.' Lucic won an Australian Open doubles title with Martina Hingis at age 15 to become the youngest Grand Slam champion but years later fled her father with the rest of her family to the United States, saying he physically abused her. 'It was just unfortunate why I haven't played,' Lucic said. 'My dream never died and never went away. I was just waiting for an opportunity. I have it. I've been living my dream.' 