In a difficult battle against the Belarusian Victoria Azarenka, the American Serena Williams came back Sunday to win her fourth U.S. Open women's singles title in a hotly contested three-set match -- 6-2, 2-6, 7-5 -- at Arthur Ashe Stadium in Flushing Meadows in New York.

Azarenka, 23, ranked No. 1 in the world, was seeded No. 1, while Williams, 30, ranked No. 4 in the world, was seeded No. 4, as the U.S. Tennis Association followed the WTA rankings to determine the seedings at the event this year.

Despite Williams' win -- her 15th in grand-slam tournament finals -- Azarenka will continue to be ranked No. 1 in the world, at least for now.

Williams is in fourth place among women's singles players during the open era for most grand-slam titles, according to the WTA. Steffi Graf, with 22, is followed by Chris Evert and Martina Navratilova, with 18 each.

Williams has won five Australian Opens (2003, 2005, 2007, 2009, 2010), one French Open (2002), five Wimbledons (2002, 2003, 2009, 2010, 2012), and four U.S. Opens (1999, 2002, 2008, 2012), the WTA said.

The tennis player has had a fantastic year, as she dominated not only at Wimbledon but also at the London 2012 Olympic Games, proving herself to be one of the greatest in the history of the game.

The match between Williams and Azarenka was the first U.S. Open women's championship match to go three sets since 1995. The match also made Williams the oldest women's singles champion at the U.S. Open in almost 40 years.

After the match, Williams said: I honestly can't believe I won. I was really prepared for my runner-up speech, because she was playing so great. I'm really shocked right now.  But Azarenka said: Serena really deserved to win. She showed how true of a champion she is, and I'm honored to stand with such a champion.

The U.S. Open will conclude Monday with the Scottish Andy Murray, who won the men's singles title at the Olympic Games, facing the Serbian Novak Djokovic, who lost to Murray in a semifinal match at those same games.