The 29-year-old defeated Vinci, who reached the final at Flushing Meadows last year, 7-5, 6-0 to boost her chances of overtaking Serena Williams as world No1 at the end of the tournament.
Williams must reach the final in New York to have any chance of staying the highest-ranked woman in the world, while if the two meet, the American would have to prevail.
“When I was a kid I was always dreaming of being the No1,” said second seed Kerber. “Let’s see. I mean, there are still matches to go. Also, Serena has to play as well very good.
“I’m looking forward to play, first of all, my next match. If the day will come, it will be amazing.”
France’s 10th seed Gael Monfils, meanwhile, dominated fellow countryman Lucas Pouille to win in straight sets, 6-4, 6-3, 6-4 and secure his first grand slam semi-final appearance since the French Open in 2008.
“It’s a court I love,” said Monfils, who is yet to drop a set in five matches at this year’s US Open. “I always say that the French is my home, but this one is my second.”