NEW YORK — Serena Williams was let down by her serve at times but not by her nerves Sunday in the U.S. Open women’s final.

Coming from behind in the third set, Williams won her fourth U.S. Open championship and her 15th Grand Slam title.

After trailing 5-3 in the final set, Williams beat No. 1-ranked Victoria Azarenka, 6-2, 2-6, 7-5. After the last point Williams dropped to the ground and let loose with a powerful yell. This was her first U.S. Open title since 2008.

She has won Wimbledon, the Olympics and the U.S. Open in the last 10 weeks, but Williams said she didn’t expect this victory after she fell behind in the third set.

“I honestly prepared my runner-up speech,” Williams said.

Azarenka earned what seemed to be the definitive service break in the seventh game of the third set. She did it by winning all four points, and when she held serve in the next game to take a 5-3 lead, it appeared the Belarusian, who won the Australian Open at the start of this year, was in position to win her first U.S. Open championship.

But Williams, who will be 31 on Sept. 26, kept playing aggressively. Azarenka, 23, had a chance to serve out the match in the 10th game but Williams broke to tie the set at 5-5 with the help of two big forehand winners.

Williams started quickly in the match, winning the first three games. After holding serve with an ace for a 1-0 lead, Williams earned a service break when Azarenka sent a forehand long.

Azarenka could never get a break point against Williams’ serve in the set. She made it to deuce in the fifth game but Williams held with a big forehand winner.

In the final game of the first set, Williams broke Azarenka at love. In that game Azarenka started with a double fault and from there Williams seemed to play with no caution. She won the second point with an explosive overhead, the third with a sizzling backhand return winner and set point with another huge backhand winner.

For the first set, Williams had 16 winners to only two for Azarenka. And Williams was 48-1 this year in matches when she won the first set.

But Azarenka started to crawl back into the match by breaking Williams’ serve to start the second set. It was only the third time during the tournament that Williams lost her serve, and she served a double fault on break point.

In the third game of the second set with Williams up 40-0 on her serve, she was called for a foot fault. The Arthur Ashe Stadium crowd gasped. During a semifinal match against Kim Clijsters in 2009, Williams was called for a foot fault and she unleashed a nasty tirade against the lineswoman who made the call. Sunday, Williams gave the linesman who made this call a long stare before she lost the next two points. But Williams held serve with an ace, though she still trailed, 2-1.

Azarenka saved a break point in the next game when Williams made a forehand error. Azarenka went ahead 4-1 with another service break in the fifth game. Williams saved three break points in that game but on the fourth, a Williams forehand sailed long and Azarenka had a 4-1 lead. Williams yelled, “Oh my God.”

Williams held serve in the seventh game with the help of two aces but she still trailed, 5-2. When Azarenka held serve, despite two double faults in the eighth game, the U.S. Open women’s final was headed to a third set for the first time since 1995.

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