Serena Williams was asked last week what the number 18 meant to her.

“It means legal to do some things,” she said, laughing.

But she knew what the reporter was getting at.

“It also means legendary,” she added more seriously.

She would not go so far as to call herself legendary — “I’m just Serena,” she said — but she joined some elite company Sunday, when she tied Chris Evert and Martina Navratilova with her 18th Grand Slam singles title.

The top-ranked Williams defeated Caroline Wozniacki, 6-3, 6-3, to capture her third United States Open final in a row and sixth over all.

Williams had not advanced past the fourth round of a Grand Slam tournament this year, and over the last two weeks she had expressed relief and excitement at her success at the U.S. Open. When Wozniacki’s final stroke went long Sunday, Williams collapsed on her back and started to cry. In a postmatch interview, she choked up saying the word 18.