By Steve Ginsburg

NEW YORK (Reuters) - Vera Zvonareva played far from her best but the world's second-ranked player gritted her teeth down the stretch to oust scrappy Ukrainian Kateryna Bondarenko on Wednesday and advance to the third round of the U.S. Open.

"I didn't play my best tennis, but I managed to get through this one," Zvonareva said after the 7-5 3-6 6-3 victory on a sunny afternoon at Flushing Meadows. "I gave myself another chance to go out there and try to do a little bit better."

Bondarenko forced a decisive set by winning the last three games of the middle frame.

The unseeded Ukrainian broke Zvonareva to get back on serve at 3-4 in the final set, raising some eyebrows at Arthur Ashe Stadium, but she was broken at love in the next game.

Zvonareva, who lost to Kim Clijsters in the 2010 U.S. Open final, needed an 11-point game to close out the two-hour, seven-minute match against the 69th-ranked Bondarenko.

The Russian said it is important to "get through those matches" when you are struggling.

"If I look back, I always don't play my best tennis in the first or second round," she said. "Never happened. And the same last year. I'm not worried about it.

"I don't play my best tennis every week. I managed to win couple of tournaments this year without playing my best."

Zvonareva had 46 unforced errors and successfully landed only 58 percent of her first serves. She won all 14 points in the opening set when venturing to the net but generally abandoned the strategy the rest of the way.

"I should have taken more risk in the second and third set, but I felt like I was a little bit off my rhythm," she said. "With the wind I could have gone to the net a bit more, and against the wind maybe I should have tried.

"Sometimes I felt like I was trying at the wrong times. She would give me a deep ball and I tried to attack it, come into the net, and she would hit a good passing shot."

Zvonareva will now face Anabel Medina Garrigues of Spain, who defeated Briton Laura Robson 6-2 6-3 in her second-round encounter. Zvonareva holds a 3-1 lifetime edge but the two have not met since 2008.

"She's very dangerous," said Zvonareva. "Definitely it's going to be a tough one."

(Editing by Frank Pingue)