The 36-year-old needed just 71 minutes to claim a 6-1, 6-2 victory at Flushing Meadows in New York.

Williams, chasing a seventh US Open title, proved far too strong for her sister in the 30th meeting between the formidable pair.

Estonia's Kaia Kanepi, a 6-3, 7-6 winner over Sweden's Rebecca Peterson, awaits for Williams in the last 16.

"This was my best match since I have returned," the American said.

"She's my best friend, she means the world to me and she's so supportive of my career and I'm extremely supportive of her career.

"Every time she loses I feel like I lose. 

"I love her with all my heart and she's the only reason I'm still out here. 

"I owe everything to her."

Elsewhere in the women's singles draw, defending champion Sloane Stephens joined Williams in round four with a 6-3, 6-4 win against two-time Grand Slam champion Victoria Azarenka of Belarus.

Home player Stephens will play 15th seed Elise Mertens of Belgium for a place in the quarter-finals.

Ukrainian seventh seed Elina Svitolina is also through after she beat China's Wang Qiang 6-4, 6-4.

Defending men's champion Rafael Nadal was made to work hard for his spot in the next round before he eventually emerged victorious from a tough contest with Russia's Karen Khachanov.

The top seed needed four sets to get past Khachanov as he won a see-saw encounter 5-7, 7-5, 7-6, 7-6.

The Spanish 17-time Grand Slam champion will next face Georgian Nikoloz Basilashvili.

Austrian ninth seed Dominic Thiem made his frustration evident during his 3-6, 6-3, 7-6, 6-4 victory over American Taylor Fritz as he broke his racquet after smashing it onto the court.