Second seed and defending champion Yanina Wickmayer demolished Simona Halep of Romania 6-0 6-2.
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She will face France's former Wimbledon finalist Marion Bartoli, who beat Yanina Wickmayer 6-4, 7-5.
Bartoli, meanwhile, reached her first WTA final in two years after thrashing Belgium's Yanina Wickmayer.
Henin will next play fellow Belgian Yanina Wickmayer, who defeated Italy's Sara Errani 6-1 6-7 (4-7) 6-3.
Peer was joined by third seed Yanina Wickmayer of Belgium, and Italian duo Francesca Schiavone and top seed Flavia Pennetta.
In Austria, Belgian second seed Yanina Wickmayer will play France's No. 2 Alize Cornet in Sunday's final of the Bad Gastein tournament.
Top seeds Maria Sharapova and Yanina Wickmayer advanced with wins over Renata Voracova (6-3 7-5) and Sabine Lisicki (6-2 3-6 6-2) respectively.
Craybas will next face Yanina Wickmayer after the unseeded Belgian crushed former teen prodigy Nicole Vaidisova of the Czech Republic 6-1 6-1.
Belgian 28th seed Yanina Wickmayer , who won the the Hobart International title last week, lost 7-5 6-2 to Kazakhstan's 62nd-ranked Galina Voskoboeva.
The 21-year-old will play another surprise winner, Latvia's Anastasija Sevastova, in round three after her 6-4 6-2 win over Belgium's 21st seed Yanina Wickmayer.
In New Zealand, third seed Yanina Wickmayer shrugged off her difficult end to 2009 by winning the ASB Classic in Auckland on Saturday.
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.
Peer, who beat 13th seed Yanina Wickmayer of Belgium in the first round, defeated last year's losing finalist Virginie Razzano of France 6-2 6-2.
Kirilenko will meet third seed Agnieszka Radwanska of Poland in the quarter-finals, while top seed Samantha Stosur of Australia will play Yanina Wickmayer of Belgium.
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On the same side of the draw, Zvonareva is next up against unseeded Belgian Yanina Wickmayer, who beat American wildcard Jill Craybas 7-6 (7-2) 6-1.
The second seed beat Klara Zakopalova from the Czech Republic 7-6 6-0 to set up a meeting with Kerber who beat Yanina Wickmayer from Belgium 6-7 6-3 6-4.
The 21st seed was upset 6-3 7-5 despite battling back from 3-0 down in the second set, with Vinci earning a third-round clash with Belgian 13th seed Yanina Wickmayer.
The seventh seed followed up her demolition of No. 11 Yanina Wickmayer by crushing Venus Williams 6-0 6-1 in Thursday's late match, inflicting the fourth seed's worst defeat of her distinguished career.
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Two-time Indian Wells champion Daniela Hantuchova saved two match points at 5-6 down in the third set of her second round meeting with Yanina Wickmayer before she edged through 5-7 6-3 7-6 (7-4).
Hungary's Agnes Szavay walked into the second round when Olga Govortsova of Belarus retired hurt while trailing 6-3 1-0, and will face third seed Yanina Wickmayer in the second round if the Belgian beats Croatian wildcard Petra Martic.
The third seed made light work of Japan's Ayumi Morita 6-1 6-3 to set up a fourth round tie against 14th seed Maria Kirilenko from Russia who was also a straight sets winner (7-6 6-3) over Belgium's Yanina Wickmayer.
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