Melbourne:Serena Williams advanced to the semi-finals of the Australian Open, overcoming a sluggish start on Tuesday and a seesawing third set to beat Shahar Peer 3-6, 6-2, 8-6. Williams has now won five consecutive matches for the first time since she captured the last of her seven Grand Slam singles titles here two years ago. "I am the ultimate competitor," a relieved Williams said after the match. "I feel awesome. I'm excited to be out here ... I'm just so happy to be back out here competing," she said. The 25-year-old American, who played only four tournaments last year due to a recurring knee injury, dropped her first service game. She was down the break for the rest of the first set, fending off a set point in the eighth game and two more in the ninth before Peer won it with a big first serve. 'Helpful' notebook Peer had only lost one point on her own serve in the second set until 30-love in the sixth game, when Williams ran off four straight points to go ahead 4-2. The first four games of the deciding set took 34 minutes - four minutes longer than the entire second set - with Williams saving break points in the first and third games and then breaking the 16th-seeded Peer in the fourth. But just when the former No 1 seemed to have the match under control, Peer rallied and got the set back on serve. Williams faced double break point in the ninth game, saving both with aces and then closing for a 5-4 lead with an other down the middle. Peer broke again in the 11th game and the 19-year-old Israeli was serving for the match before Williams broke back and then held at love for a 7-6 lead. In the changeover, Williams quickly flicked through a notebook. Whatever she read must have helped. She came out and broke serve again, winning on her first match point when Peer curled a backhand out after 2 hours and 34 minutes. Williams had 49 unforced errors and only 30 winners. But in the end, her experience counted most. Williams converted five of her six break-point chances, while Peer converted only three of 13. Williams next plays 17-year-old Nicole Vaidisova, who beat fellow Czech Lucie Safarova 6-1, 6-4 earlier on Tuesday to reach her second Grand Slam semi-final.