The defending champion, who was knocked out of the Australian Open by her opponent at the start of the year, advanced to the fourth round with a 6-4 6-1 win over Stephens at Flushing Meadows.
Williams, who won eight of the last night games, admits that she was relieved to overcome a difficult challenge in the form of Stephens.
"She's definitely a good player, so it felt like something bigger, but I just had to stay focused for the moment," Williams told reporters.
"The whole time I just tried to do what I wanted. Stay calm, stay relaxed, stay composed."
Williams now faces Carla Suarez Navarro in the last eight.