The tournament's third seed dropped the first set 4-6 and was broken in the first game of the second before staging the comeback.
"I wasn't great, for sure," Kvitova said. "I wasn't feeling very well. I wasn't positive during the game and then I had to fight and try to come back in the match."
She broke serve to close out the match, which had been pushed back a day because of rain Monday night.
Beck entered the draw as a lucky loser when Poland's Urszula Radwanska withdrew Monday with what was described as a viral illness.
"It was a long day yesterday for sure, for both of us," said Kvitova. "It was a little bit different, but it was the same for both of us, so I can't say that the beginning of the match was because of yesterday."
The 2011 Wimbledon champion wasn't the only seeded player to struggle. Second-seeded Angelique Kerber lost her second-round match 6-2, 6-4 to Russia's Elena Vesnina. Seventh-seeded Sabine Lisicki fell 7-5, 6-3 to Anastasia Pavlyuchenkova in the final match of the night.
Four of the tournaments eight seeds have been eliminated in the first two rounds.
Kerber, ranked 10th in the world, was making her first appearance in New Haven after drawing a first-round bye.
Vesnina, a 2009 finalist, won the first three games to take control of the first set. She broke serve for the sixth time in the final game of the match. Kerber hit a forehand just wide on match point and threw her racket in disgust. The call was upheld after a challenge.
"I knew that she would not have, like, a big serve," said Vesnina. "I was just trying to be focused on these returns and waiting for the second serve to attack, step in and move her around."
Vesnina, seeking her third singles title this year and third of her career, said the win over a top-10 opponent bodes well for her heading into next week's U.S. Open.
"Maybe it's just my time to play good," she said.
Kerber, who lost in the third round in Cincinnati and the second round in Toronto, had hoped to get in a couple more hard-court matches to improve her game before the Open.
"It's, of course, not easy to lose a match like this when you are not feeling so good and you couldn't find your rhythm," she said. "Next week is a big tournament, but I will try to go on the court tomorrow and work and try to improve my game more. I will try to take my rhythm back."
When asked what part of her game needs to be fixed, she said, "I think right now, everything."
Vesnina will face Klara Zakopalova of the Czech Republic in the quarterfinals. Zakopalova upset eighth-seeded Dominika Cibulkova in the first round before beating 19-year-old Monica Puig 6-4, 6-1 on Tuesday.
Her recent strong play earned her the 32nd and final seed next week at Flushing Meadows.
"I have never passed the first round at the U.S. Open," she said. "So, my goal is to play a good first round there and then we'll see."
It was their fourth tournament together since Hingis announced her comeback, and the Swiss star said she is not planning to expand her return to singles play.
"I have always said that I don't want to play singles anymore, for sure," she said. "And after tonight, it's definitely 200 percent, no way. Because, you just have to be so hungry."