Pliskova, 22, took advantage of a slew of miscues from the eighth-seeded Serb during a windy, 80-minute match in Louis Armstrong Stadium to reach the third round for the first time in a grand slam event.
Ivanovic, 26, double-faulted seven times and committed 29 unforced errors as she had trouble handling the heavy, flat groundstrokes from the Czech.
"It's definitely my best match this year," said Pliskova, who has yet to win on the WTA Tour but twice has been a runner-up this year.
"I didn't have that much strategy. I just went and played my game. I want to enjoy myself and I did it."
Ivanovic began the year's fourth and final grand slam full of confidence after a runner-up finish in the Cincinnati tune-up event.
"It was very tough out there for me today," said Ivanovic, who has wins over Serena Williams and Maria Sharapova this season in battling back into the world top 10.
"I really struggled to find my rhythm and made way too many unforced errors. It was just really a bad day."
Pliskova, the 2010 Australian Open girls' champion, has been making tour progress in singles after gaining attention for her success in doubles, partnering with twin sister Kristyna last year to become the first twins to ever win a WTA doubles title.
"My serve, that's the main point," said Pliskova, who had seven aces in subduing Ivanovic.
"I was serving well. But I was trying to play aggressive. I knew if I was not going to be that aggressive she was going to make more winners than I, so I was trying to stay aggressive and to go to every point.
"She did a few mistakes which I think was the deciding point."
Pliskova will next meet 29th seed Casey Dellacqua of Australia, who overcame China's Wang Qiang 4-6 6-4 6-2.
(Reporting by Larry Fine; Editing by Frank Pingue)
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