NEW YORK — Finally tested, even trailing, at the US Open, Serena Williams turned things around just in time.

Two points from defeat, Williams suddenly regained her composure and her strokes, coming back to win the last four games and beat top-ranked Victoria Azarenka, 6-2, 2-6, 7-5, Sunday night for her fourth championship at Flushing Meadows and 15th Grand Slam title overall.

‘‘I honestly can’t believe I won,’’ Williams said during the trophy presentation after the 2-hour-18-minute match. ‘‘I really was preparing my runner-up speech, because I thought, ‘Man, she’s playing so great,’ I’m really shocked.’’