Big-serving Czech Pliskova reached the top of the rankings a year ago at Wimbledon despite losing in the second round -- the fifth year in succession she had lasted only two matches.
From the moment Azarenka dropped serve with a loose error in the third game, Pliskova always looked likely to break that sequence against the Belarussian who is still trying to rediscover her past form after returning from having a baby.
Azarenka tried to fire herself up when she resisted some pressure to hold serve at the start of the second set.
But Pliskova broke for a 5-3 lead and was then helped by two Azarenka double faults that brought groans from the sedate crowd who had been hoping for something more exciting.
"I think I was pretty solid today, I think I was really strong on my serve which was really important," the 26-year-old Pliskova said after walking off court.
"Very happy with my victory as it is the first time I am in the third round here. The last few years I was waiting for a good result and it still didn't come, maybe this year is the time; I am feeling great."
She will play Romanian 28th seed Mihaela Buzarnescu next.
(Reporting by Martyn Herman)
