The victory represented Williams 307th Grand Slam title, more than any other woman in the sport, eclipsing Martina Navratilova. Shvedova is best known for the first "golden set" in the Open era, which began in 1968: She won all 24 points of the first set of a victory over Sara Errani at Wimbledon in 2012, one match before a three-set loss to Williams there.
"I think I was playing good tennis from the beginning", she said.
Del Potro's resurgence continued with a 7-6 (7-3), 6-2, 6-3 victory over No. 11 David Ferrer.
World No. 1 Serena Williams needs to outlast world No. 2 Angie Kerber to keep her top ranking during this fortnight at the US Open.
"It is me", Williams said, smiling. Turns out, though, that NY is proving a very special place for an athlete who was retired at this time two years ago.
Fifth seed Simona Halep of Romania made hard work of her encounter with Hungary's Timea Babos before eventually ending on the right side of a 6-1, 2-6, 6-4 scoreline, while Poland's Agnieszka Radwanska, seeded fourth, beat Caroline Garcia 6-2, 6-3. "I think that's what matters most for me".
The media wing talked to her after reaching this landmark. I started to feel better more consistently this year, so I'm always trying to find things to help me feel my best. This is the 14th time she has reached last 16 at Flushing Meadows.
It's Venus time! The elder of the Williams sisters, Venus Williams, 36, takes on Laura Siegemund, 28, on September 3 at 7pm EST in round 3 of the United States open at USTA Billie Jean King National Tennis Center.
Not only has world No. 1 surpassed Navratilova, she matched Roger Federer's mark for men. He's had four tour wins and a run to the French Open semifinals this year.
Six-time US Open champion Serena Williams eases past Johanna Larsson to reach the fourth round of the 2016 US Open.
Serena Williams faced Sweden's Larsson, who she had beaten in straight sets in both previous meetings. Stan Wawrinka held off an upset bid by Briton Dan Evans, winning 4-6, 6-3, 6-7 (6), 7-6 (8), 6-2. She opened up to a 3-0 lead in the first set against an overmatched Larsson and never looked back.
Murray faces Grigor Dimitrov next up, who advanced to the fourth round courtesy of a 6-4 6-1 3-6 6-2 triumph over Joao Sousa.
Halep is due to go up against Spaniard Carla Suarez Navarro, with Radwanska due to face Ana Konjuh of Croatia. Sister Venus, the sixth seed and oldest woman in the tournament at 36, plays later in Ashe against 26th-seeded Laura Siegemund of Germany.
Nick Kyrgios, the 14th-seeded firebrand from Australia, closes the show on Ashe against Illya Marchenko a Ukrainian ranked 47 spots below him.
Juan Martin del Potro, whose career was almost derailed by injuries after his 2009 US Open triumph, fired 37 winners in a 7-6 (7/3), 6-2, 6-3 victory over Spanish 11th seed David Ferrer.