World No 1 Serena served well in moving within three match victories of a 2015 sweep of major titles by defeating US 19th seed Madison Keys 6-3, 6-3.
Serena, who struggled with her serve in two prior triumphs, hit 58 percent of her first serves and made only six unforced errors to 19 for Keys. She took 70 percent of points on her second serves, nearly twice Keys' second-try effectiveness.
"My serve was definitely better. I also was hitting them a lot harder than I normally hit them," Serena said. "My only chance was to start out fast. I just stayed in there and was able to relax."
Venus, seeded 23rd, downed 152nd-ranked Estonian teen qualifier Anett Kontaveit 6-2, 6-1 at Arthur Ashe Stadium, matching her deepest Grand Slam run since reaching the 2010 US Open semifinals.