And ninth seed Daniela Hantuchova saw off France's Alize Cornet 6-2 7-5 to continue her progress.
Martinez will next take on Patty Schnyder, who beat Daniela Hantuchova 6-7 6-3 7-6 on Friday.
Thirteenth seed Daniela Hantuchova went through after three tough sets against Luxembourg's Anne Kremer.
Other seeded players to progress were China's Na Li (16), Daniela Hantuchova (22) and Shahar Peer (29).
Fifth-seeded Italian Sara Errani also lost in three sets to 2012 runner-up Daniela Hantuchova 4-6 6-1 7-5.
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Meanwhile, defending champion Serena Williams cruised into the quarterfinals with a crushing 6-2 6-0 win over Slovakian Daniela Hantuchova.
Actress Jessica Alba , tennis player Daniela Hantuchova and socialite Paris Hilton were Nos. 2, 4 and 5, respectively.
Slovakia took an unbeatable 3-1 lead against last year's finalists Serbia as Daniela Hantuchova won 6-3 6-2 against Vesna Dolonc.
Also on Wednesday, Japan's Ai Sugiyama ousted fourth-seeded Daniela Hantuchova of Slovakia 6-3 6-1 to advance to the last eight.
Slovak number seven seed Daniela Hantuchova was defeated in a three-set marathon with Spaniard Arantxa Parra Santonja 6-4 6-7(7-3) 7-6 (7-5).
Daniela Hantuchova, another two-time champion, was knocked out by Italy's Roberta Vinci.
Fourth seed Stosur reached the final of the Family Circle Cup with a 6-3 7-6 (7-2) victory against No. 8 Daniela Hantuchova of Slovakia.
Daniela Hantuchova brought Slovakia level at the end of day one of the Fed Cup final with a comprehensive win over Spain's Magui Serna.
Ekaterina Makarova and Elena Vesnina won the deciding doubles rubber, beating Dominika Cibulkova and Daniela Hantuchova 4-6 6-3 6-1 in two and a half hours.
Williams, who had required three sets to defeat Daniela Hantuchova in the previous round, was delighted to have had an easier ride this time around.
Clijsters will next face German Andrea Petkovic, who secured her last-four spot with an upset 6-4 6-2 victory over fourth seed Daniela Hantuchova of Slovakia.
Nigel Sears, former coach to Daniela Hantuchova, has been brought in by Maes to work with the key players and captain the Fed Cup side.
Serena now faces Daniela Hantuchova, with Venus up against Kim Clijsters.
Clijsters, who will now face eighth seed Daniela Hantuchova or the unseeded Elena Dementieva in Sunday's final, broke first in the third game of the match.
In Friday's third and final match, Slovakia's Daniela Hantuchova beat world number two Svetlana Kuznetsova 7-6 6-0 in a consolation match between the two eliminated players.
Third seed Daniela Hantuchova cruised past unseeded Slovakian compatriot Dominika Cibulkova 6-1 6-4 and will now play 13th seed Sybille Bammer, who beat Karolina Sprem 6-2 6-3.
The three-time champion, who is unbeaten in 12 matches after winning two successive tournaments, will next face either Russian 16th seed Nadia Petrova or Slovakia's Daniela Hantuchova.
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Fifth seed Dementieva, who won the Paris Indoor Open title on Sunday, suffered a shoulder injury in her match against Daniela Hantuchova and pulled out while trailing 6-4 1-1.
Dominika Cibulkova beat Anastasia Pavlyuchenkova 5-7 6-1 6-4, and then Daniela Hantuchova defeated Maria Kirilenko 6-2 6-4 as the Slovakians seek to reach their first final since winning the 2002 title.
Seventh seed Vera Zvonareva defeated ninth seed Alona Bondarenko 6-2 6-1, 13th seed Melanie Oudin beat Christina Mchale 6-4 6-0, and eighth seed Daniela Hantuchova battled past Angelique Kerber 6-7 (6-8) 7-5 6-3.
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).
The young Briton had taken former world number five Daniela Hantuchova to three sets on her senior Wimbledon debut 12 months ago, but stepping on to Centre Court for the first was a different experience entirely.
Spanish 26th seed Anabel Medina Garrigues went through 6-3 6-3 against Czech Eva Birnerova, while Slovakian 20th seed Daniela Hantuchova recovering from dropping the opening set to Uzbekistan-born American Varvara Lepchenko to win 4-6 6-3 6-2.
Daniela Hantuchova had earlier won 7-5 6-2 against Bojana Jovanovski, elevated to No. 1 in the home Serbian team due to the late withdrawals of former world No. 1s Ana Ivanovic and Jelena Jankovic through injury.
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