By reaching the last eight Kerber has put herself in position to end Serena Williams' long reign as world number one.
Williams, bidding for a record seventh U.S. Open title, will now need to reach the final to have a chance of retaining top spot.
"When I was a kid, of course I was dreaming to winning slams and being one day number one," admitted Kerber. "Now it can happen.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I'm trying to not put pressure on myself because I know I have to win few more matches to reach the number one.
"When it's happen it will be amazing feeling because that was also one of my dreams.
"But let's see what happens here in the next few days."
The fourth-round match had a grand slam pedigree to it with Kerber, the Australian Open champion, going against twice Wimbledon winner Kvitova, but it failed to deliver any major excitement.
To be fair, Kerber and 14th-seeded Kvitova were handed a tough act to follow with the capacity Arthur Ashe Stadium crowd left buzzing about Frenchman Lucas Pouille's upset win over Rafa Nadal in a five-set thriller that had closed out the day session an hour earlier .
Kerber was in command from the start, winning all the big points on the way to taking the opening set.
Kvitova, the Rio Olympics bronze medallist, offered more resistance in the second before surrendering with a double fault on match point to gift Kerber a place in the quarter-finals.
"I felt I played a little terrible, to be honest," said Kvitova. "It wasn't really nice tennis.
"I was trying. I felt like that I really made the chances but I just didn't take them unfortunately."
Kerber's victory set up a last eight clash with Italy's Roberta Vinci, last year's surprise runner-up, who advanced with a 7-6(5) 6-2 win over Ukraine's Lesia Tsurenko.
(Editing by Andrew Both/Peter Rutherford)
