The sixth-seeded Vaidisova, currently ranked 41st, took 2 hours, 27 minutes to beat Alla Kudryavtseva of Russia 7-6 (3), 4-6, 7-5.
The 19-year-old Czech player, winner of six WTA singles titles, led 4-0 in the third set before briefly losing her way against the 71st-ranked Kudryavtseva.
She squandered two match points at 5-3 but converted her third in the 11th game of the set.
"It's hard when you know you've had two match points on your serve,'' said Vaidisova, who injured her right wrist last year. "But I tried to hang in there, especially mentally.
"It's the first week and I don't think you pay as much attention to how (your opponent) plays as what you're trying to do. You try to do things that you practiced for two months.''
Fourth-seeded Aleksandra Wozniak of Canada beat Slovakia's Magdalena Rybarikova 6-3, 6-7 (4), 7-5 on a day in which all four seeded players advanced to the second round.
Third seed Anabel Medina Garrigues of Spain beat Italy's Mara Santangelo 7-5, 6-0 and No. 5 Shahar Peer of Israel beat Petra Cetkovska of the Czech Republic 7-6 (4), 6-2.
In a match between unseeded veterans, American Jill Craybas, 34, beat Japanese wild card Kimiko Date Krumm, 6-3, 6-4.
The 38-year-old Date Krumm, formerly ranked No. 4 and now 189th, was playing her first professional tournament outside Japan since ending a 12-year retirement in May.
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