While the Czech converted both of her break point opportunities, 18th seed Barty was left frustrated time and again as she failed to capitalise on her chances.
Pliskova, who was a finalist at Flushing Meadows in 2016, committed 20 unforced errors to Barty's 30, and closed out the match when her opponent smacked the ball into the net.
"It was very tough even though the score looks easy," Pliskova said in an on-court interview. "I’m very happy to be through."
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.
She added to reporters later: "I didn't have that many chances because of her game.
"I didn't really feel like I had the chance and time to be aggressive.
"She had a lot of break points, so it could (have) gone both ways today. It was really like couple points."
Pliskova will next face Serena Williams.
The last time the players met, Pliskova toppled the American to reach the U.S. Open final in 2016.
Pliskova will be hoping she can draw on that experience to secure her passage into the semis.
"I really was feeling great that year. I'm feeling great now, too. But it was a little bit different story, 2016. I was, like, dark horse. Nobody was expecting me to get that far," Pliskova said.
"I know she has a big game, but I have a big game too. I have a good serve. So I have some weapons too. There is always a chance for me."
(Reporting By Amy Tennery, editing by Pritha Sarkar)
