The French 17th seed, herself another former No. 1, won 7-5 6-3 against 15th-seeded Italian Flavia Pennetta earlier on Saturday.
Flavia Pennetta and Francesca Schiavone claimed singles wins over Anna Chakvetadze and Svetlana Kuznetsova in Castellaneta Marina in southern Italy.
Peer was joined by third seed Yanina Wickmayer of Belgium, and Italian duo Francesca Schiavone and top seed Flavia Pennetta.
Italian 14th seed Flavia Pennetta defeated Romania's Sorona Cirstea 6-1 1-6 6-1 to earn a second-round clash with German Andrea Petkovic.
Swiss player Schynder dropped the opening set against Flavia Pennetta of Italy but came back strongly to win 4-6 6-0 6-1.
The winner of that match will play either fifth seed Petrova or last year's losing finalist, 10th seed Flavia Pennetta of Italy.
The Italians, led by 2010 French Open champion Francesca Schiavore and world No.22 Flavia Pennetta have won four of their last seven meetings.
CNN: Fed Cup: Serbia makes history in first semifinal showdown
But their compatriot Flavia Pennetta made a shock early exit as the 19th seed lost 6-3 1-6 6-2 against Russian qualifier Nina Bratchikova.
Seventh-ranked Elena Dementieva will take the American's place as top seed, with Italian No. 12 Flavia Pennetta second and Yanina Wickmayer of Belgium third.
The second seed will now play Italian Flavia Pennetta for a place in the quarterfinals after she beat seventh seed Vera Zvonareva of Russia.
Hungary's Agnes Szavay progressed to the second round after Italian fourth seed Flavia Pennetta was unable to complete their match despite winning the first set.
With a 2-0 lead overnight, world No. 11 Flavia Pennetta's 7-5 6-2 victory over Melanie Oudin in Sunday's opening singles match gave the Italians an unassailable lead.
The final takes place on 7-8 November in Reggio Calabria, Italy, and the hosts will be represented by Flavia Pennetta, Francesca Schiavone, Roberta Vinci and Sara Errani.
After Italy claimed both singles rubbers on Saturday, world No.15 Flavia Pennetta won her second match on Sunday to ensure her nation will contest November's climax to the tournament.
Ninth seed Flavia Pennetta also went through with a 6-3 6-3 win over Czech Petra Kvitova, and the Italian will play Israel's 17th seed Shahar Peer in the third round.
Seeds Agnieszka Radwanska, Flavia Pennetta, Alisa Kleybanova, Agnes Szavay, Sybille Bammer and Aleksandra Wozniak also advanced, but Alize Cornet, Dominika Cibulkova, Zheng Jie, Ai Sugiyama and Sara Errani failed to progress.
Tenth seed Shahar Peer completed a routine 6-3 6-2 victory over Romania's Sorana Cirstea to secure a match against Italy's 22nd seed Flavia Pennetta , who beat Spain's Lourdes Dominguez Lino 6-2 6-2.
In the WTA tournament, ninth seed Serena Williams had an easy passage to the last four when her Italian opponent Flavia Pennetta retired with a wrist injury when trailing 4-0 in the opener.
The 20-year-old Belgian, who won her appeal against a one-year ban for failing to report her whereabouts for doping tests, defeated top seed Flavia Pennetta 6-3 6-2 to clinch her third WTA Tour title.
Number 14 seed Flavia Pennetta demolished her fellow Italian Roberta Vinci 6-1 6-1, 19th seed Nadia Petrova was similarly comfortable in her 6-1 6-2 win against Agnes Szavay, and Alexandra Dulgheru eased past Timea Bacsinszky 6-4 6-2.
One upset of the afternoon came courtesy of Italian qualifier Carmila Giorgi, who beat compatriot and No. 16 seed Flavia Pennetta 6-4 6-3, while No. 27 seed Daniela Hantuchova was beaten 6-4 7-6 by American Jamie Lee Hampton .
Former world No. 1s Kim Clijsters and Ana Ivanovic will meet in round three, while Czech sixth seed Petra Kvitova -- whose Wimbledon defense was ended by Serena Williams in the quarterfinals -- will take on Italy's Flavia Pennetta.
应用推荐