The unseeded American, twice a winner at Melbourne Park, looked shaky in the first set and Peer took advantage. However, Williams battled back, winning eight out of nine games from 2-2 in the second set to seemingly take control. Peer, the 16th seed, fought back in the final set and even served for the match before a fired-up Williams finally won 3-6 6-2 8-6 in a thrilling clash in the Rod Laver Arena.

Despite heading into the quarter-final on the back of a stunning win over in-form Serbian Jelena Jankovic, Williams looked in trouble early on as Peer converted a break point to take the first set. Wrapping it up in only 41 minutes, the Israeli was well-placed to reach her first Grand Slam semi-final until the 2003 and 2005 champion began to fire.

However, the match was far from over as the Israeli refused to concede defeat. Trading early service breaks in the final set, Peer had the chance to serve for the match at 6-5, but Williams somehow managed to break back when it mattered.

Then, after holding her next service game with relative ease, Williams broke her opponent again to seal victory with her first match point.

Speaking afterwards, the two-time Wimbledon champion said she was surprised to win. "I don't think I played as strongly [as against Jankovic]," Williams admitted. "I think I came out a little flat, started out a little slow. Maybe I was just a little nervous. I didn't have enough blood pressure in my feet. I just had to get going. I had to work my way in the match."

"I don't think anyone thought I would get this far, except for me and my mom. I wasn't playing my best tennis. I'm excited I was able to come through."

Williams will meet Nicole Vaidisova, who saw off a brave effort from her unseeded Czech compatriot Lucie Safarova 6-1 6-4, in the semi-finals.Vaidisova, the tournament's 10th seed, claimed an early lead in the first set and never relinquished her hold on the match from then on.

"It's definitely always a big key, my serve and return. I served pretty well and I'm really happy the way I returned her serve," she said. "She's tricky. She's a lefty. She can have those weird rotation slices. I read it well. I'm happy about that."