The hamstring was still strapped on Saturday as she came back to beat Azarenka in the final.
Azarenka, 31, from Belarus, lost to Serena Williams in classic U.S. Open finals in 2012 and 2013 but rallied to defeat the 38-year-old Williams in a ferociously contested semifinal on Thursday and started just as convincingly on Saturday.
Azarenka was unseeded and had not won a tour match in nearly a year before arriving in New York, but she is hardly a tennis outsider. She was No. 1 for 51 weeks in 2012 and 2013 and won two Australian Open singles titles before Williams reasserted herself at the top of the women’s game, and Azarenka dropped back.
She had injuries, painful breakups with boyfriends and coaches and, most traumatically, a lengthy and bitter custody dispute over her now 3-year-old son, Leo, who stayed with Azarenka and her mother and team at a private home she rented near the U.S.T.A. Billie Jean King National Tennis Center for the tournament.
She would have been the first mother to become a Grand Slam singles champion since Kim Clijsters won the Australian Open in 2011. As Azarenka dominated the opening set, hitting nearly every first serve in play and controlling the rallies, it appeared she might win in a hurry. Osaka threw her racket at one stage in frustration as her unforced errors piled up.