Zakopalova, from the Czech Republic, won the first Open in 2005 and was too composed for Navarro, a French Open quarterfinalist.
"Today it was very windy and it was very tough to play. I was a bit more lucky,'' Zakopalova said.
Fifth-seeded Tsvetana Pironkova of Bulgaria also lost, to Katie O'Brien of Britain 7-6 (4), 4-6, 6-2.
O'Brien was a late substitute in the main draw for Kaia Kanepi of Estonia, who had to withdraw with shin splints. She thought she'd wasted her opportunity.
"After leading 4-1 in the second set I lost five games in a row and I thought I had blown my chance, so I was really pleased I managed to regroup and the win in the third,'' O'Brien said.
The two other seeds in action were winners: Third-seeded Dane Caroline Wozniacki defeated Slovenian wild card Andreja Klepac 7-5, 6-0, and fourth-seeded Anabel Medina Garrigues of Spain beat Ekaterina Makarova of Russia 6-1, 6-3.
In other first-round matches, Vera Dushevina of Russia was a 6-3, 6-3 winner over Virginia Ruano Pascual of Spain, Croatia's Petra Martic ousted Germany's Angelique Kerber 7-5, 6-2, and Julia Vakulenko of Ukraine beat local wild card Polona Hercog of 5-7, 6-4, 6-4.
Top-seeded Maria Kirilenko and No. 2 Katerina Srebotnik both play on Tuesday.
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