But Russian fourth seed Elena Dementieva, the 2000 silver medallist, suffered a surprise 4-6, 6-0, 6-3 first round loss to unseeded Australian Alicia Molik.
All the players had to cope with difficult conditions created by the gusting wind in the morning session at the Olympic Tennis Centre.
Moya saved three match points in the final set before prevailing, sealing victory with a clubbing forehand winner after nearly three hours on a sparsely attended centre court.
The 1998 French Open champion had two match points in the second set tiebreak but in a see-saw decider Moya broke decisively for 8-7.
Dementieva, one of four Russians in the top nine seedings for the women's singles, was in control against Molik in the first set but the French Open runner-up's game deserted her as the Australian took command thereafter.
"It was pretty horrible out there," Molik said of the conditions.
Russian ninth seed Nadia Petrova, meanwhile, disposed of Slovakia's Martina Sucha 6-3, 6-3 but Sweden's Joachim Johansson upset men's 12th seed Paradorn Srichaphan of Thailand 6-2, 6-3.
Israeli 13th seed Anna Smashnova-Pistolesi, only competing after a last-minute compromise over a sponsors clash, lost 6-2, 6-1 to unseeded Tathiana Garbin of Italy.
In the men's doubles Americans Andy Roddick and Mardy Fish lost to experienced Indian pair Mahesh Bhupathi and Leander Paes 7-6, 6-3.
In Monday's evening session world number one Roger Federer of Switzerland starts his bid for a first Olympic gold against Russian Nikolay Davydenko.
The second and third women's seeds, France's Amelie Mauresmo and Russian Anastasia Myskina, are also in first round action.
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