Serena Williams hails 'big' Sloane Stephens victory

World number one Serena Williams has revealed that her victory over compatriot Sloane Stephens felt 'bigger than it was' at the US Open on Sunday.

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.