Gajdosova defeated Italian Corinna Dentoni 6-1, 6-2 but Martinez Sanchez lost in three sets 6-0, 5-7, 6-4 to Russian Ekaterina Makerova.
The unseeded Spaniard recovered after a shocking start to regain her composure on her favoured clay and take the second set but Martinez Sanchez was always behind in the decider as Makerova sealed a fine win in breezy conditions.
The Russian, ranked 37th in the world, meets her compatriot Maria Sharapova in the second round.
In further upsets, 11th-seed and twice runner-up Svetlana Kuznetsova fell in three hard-fought sets 3-6, 7-6 (7-4), 7-6 (11-9) to unseeded Hungarian Greta Arn, who, at 32, is playing the best tennis of her life.
Another former finalist Patty Schnyder succumbed 6-3, 6-2 to Spanish qualifier Ana Medina Garrigues, who next meets Marion Bartoli after the France player disposed of Arantxa Parra Santonja 6-3, 6-2.
American teenager Christina McHale's fine run continues after the qualifier dug deep to down China's Shuai Peng 6-3, 2-6, 7-6 (9-7).
The 18-year-old now faces local favourite and second seed Francesca Schiavone.
On a mixed day for Spanish players, Lourdes Dominguez Lino came through her match against Barbora Zahlavova Strycova 6-1, 0-6, 7-6 (7-4) to set up a second-round clash against fourth seed Li Na of China.
-ABC/ReutersTags: sport, tennis, italy