The No.7-seeded Kvitova, who has actually made the semifinals or better at the other three Grand Slams but has never been past the fourth round here, won a see-saw battle with Misaki Doi, 62 36 61.
"I don't think I've played that often on Ashe, so for me it was nice to be back on that court today," Kvitova said. "The wind was quite difficult for us, but it was the same conditions for both of us. It wasn't an easy match for first round - it's always tricky and difficult, so I'm glad I got through this match."
"I never played well in America before, then last year I played well when I won the US Open Series and got to the fourth round here," Kvitova said. "It's difficult to say why I've had problems here. I like Wimbledon, which is very calm, but then here it's more crowd and big show, and while I like big matches in big stadiums, maybe it's too crowded for me here. But I want to improve my results here."
"Coming into the tournament I was playing really well - I had a few tough losses, but I was very confident with my game and the way I was playing," Ivanovic said. "I was very pleased with the performance today. It was a little bit shaky in the beginning, a lot of breaks, but once I found my rhythm I sort of felt more comfortable as the match went on. I felt my game plan sort of settle in out there."
Like Kvitova, Ivanovic - who won the French Open in 2008 - has been to the semifinals or better at the first three majors, but never here. She has been to one quarterfinal here though, just last year.
Ivanovic is also a former No.1, and is hoping to break back into the Top 10 in the near future.
"It's my only goal I have at the moment - I really want to get back to the top of the game," Ivanovic said. "Once you're in the top, you don't really feel satisfied with being in the Top 15. You really want to aim higher and push yourself. That's where I'm at. And I really believe I have the qualities to do so.
"I really want to put my head down and work hard and try to maximize my potential."