Australian Open champion Angelique Kerber seeded second in the women’s draw, led Polona Hercog 6-0 1-0 when the Slovenian succumbed to leg cramps.
Kerber made it through to round two without dropping a game, as she looks to land a second major title and end Serena Williams’ 185-week run at the top of the rankings.
Kerber, 28, came within one match win of toppling the American eight days ago in Cincinnati, and Muguruza and Agnieszka Radwanska also have a chance to do so in New York.
“To be one day number one, I think this is a goal from everybody, especially also for me,” said Kerber.
“But I will not put too much pressure on myself because I know that when I put the pressure on, I’m not playing my tennis then.”