Vaidisova, one of the tournament's big names, needed two hours and 37 minutes to subdue her opponent 7-6 (7-3) 4-6 7-5.
While looking understandably scratchy at times in her first outing of the new season, the former world No 7 had seemed to be running away with the contest when leading 4-0 in the final set.
In what had then seemed to be a pivotal seventh game of the set, Vaidisova saved five break points to go 5-2 up.
But Kudryavtseva, whose ranking of 71 is 30 places below Vaidisova's, showed great fighting qualitie s, holding her serve to get to 5-3 and then saving two match points in the next game.
However, her resistance finally petered out when, at 5-6 down, her serving faltered and Vaidisova took advantage of the next match point opportunity that came her way.
Vaidisova, at 19 already the winner of six WTA Tour singles titles, is on a comeback trail of sorts after an injury-affected 2008 in w hich her ranking dropped to 41.
She said the first outing of any year was always tough because no one was quite sure of exactly what to expect after the off-season break.
Having raced to a healthy lead in the deciding set, she could sense Kudryavtseva relax and go for her shots, and she admitted that her failure to close out the match when she got her first chances had played on her mi nd.
"It's hard when you know you've had two match points on your serve," she said.
"But I tried to hang in there, especially mentally."
Vaidisova faces the winner of tomorrow's match between Russian Elena Vesnina and Japanese qualifier Aiko Nakamura.
However, she wasn't paying two much attention to the identity of her opponent, saying the early season focus was more on one's own game.
"It's the first week and I don't think you play as much attention to how they play as what you're trying to do," she said.
"You try to do things that you practised for two months."
In a battle between two veterans, American Jill Craybas, 34, beat Japanese wild card Kimiko Date Krumm, 38, 6-3 6-4.
Once the world No 4, Date Krumm was playing in her first p rofessional tournament outside Japan since coming out of a 12-year retirement last May.
Among those in singles action tomorrow are the top two seeds, Russian Elena Dementieva and Dane Caroline Wozniacki, and local favourite Marina Erakovic.
