Serena Williams broke the women's record for most grand slam singles wins as the American cruised past Johanna Larsson and into the US Open last 16. Williams took exactly one hour to see off Sweden's Larsson 6-2 6-1 and register her 307th major victory, beating Martina Navratilova's previous all-time best. She also draws level with Roger Federer on 307 and needs just one more win to own the record for both the men and women's game. Williams will now face Kazakhstan's Yaroslava Shvedova in the fourth round at Flushing Meadows as she chases a 23rd grand slam title and another spot in the history books. The 34-year-old won her 22nd major triumph at Wimbledon this summer and currently sits level at the top of the Open era list with Steffi Graf. In the last match of the day, second seed Angelique Kerber eased past American Catherine Bellis 6-1 6-1.