The fourth installment of the growing rivalry between Shahar Pe'er and Serena Williams is set to unfold in Rome on Thursday when the two players face off in the third round of the Italian Open. The Israeli, who is ranked No. 15 in the world and seeded 11th at the $1.34 million Tier I event, booked her place in the last 16 of the tournament on Wednesday by defeating Ai Sugiyama of Japan (25) 6-0, 6-2. Pe'er coasted through the second-round match, breaking Sugiyama five times and comfortably holding her serve throughout the two sets. "I played very well today," Pe'er said after the match. "In the first two games, I came back from 40-15 and 40-0 and that gave me confidence. "I moved well on the court and I hit the balls deep with a lot of topspin. I'm pleased with the way I'm playing." The Israeli will, however, face a far tougher challenge in the third round against Williams (11). The 25-year-old American, who defeated Pe'er in their first ever meeting in Miami in 2005, outlasted the 20-year-old Israeli 3-6, 6-2, 8-6, in an unforgettable Australian Open quarterfinal in January and won 7-6(4), 6-1, when they last met in the semis in Miami last month. Pe'er has come close in her matches against Williams, who has only lost twice in 2007, but has never managed to translate her good play into victories. One fact that will boast the Israeli's confidence ahead of encounter is that on Thursday the players will face each other for the first time on clay, Williams's least-favorite surface. "We all know Serena is a great player," said Pe'er. "I've never played her on clay, so it should be a good and tough match. I'm looking forward to tomorrow and I'll give everything I've got on court." On Wednesday, Pe'er only claimed the first game of the match after saving two break points, which would prove to be Sugiyama's last of the afternoon. The Israeli broke her opponent immediately in the following game and wrapped up the set in 27 minutes. Pe'er, who advanced to the second round after Agnieszka Radwanska of Poland retired from their first-round match with the score at 6-0, 2-0, lost her first game of the tournament in the second game of the second set. However, Sugiyama would only win one more game the remainder of the set and the Israeli booked another showdown with the former No. 1. In the doubles tournament, Pe'er fell at the first hurdle, losing with partner Dinara Safina 6-2, 6-4 to Daniele Hantuchova and Nadia Petrova on Tuesday.