But the hard-hitting Russian broke in the fourth game before Pliskova recovered to force a tie-break which the world number 30 emerged on top.
And with momentum on Pavlyuchenkova's side, she broke in the opening game of the second set.
Pliskova levelled up at 3-3 as she looked to mount a comeback. But in a tense battle that went to another tie-break, it was Pavlyuchenkova who booked her place in the fourth round.
Pavlyuchenkova, who had never beaten Pliskova in their previous six meetings before today's game, will face Angelique Kerber after the three-times Grand Slam champion beat unseeded Italian Carolina Giorgi 6-2, 6-7 (4-7), 6-3.
Pavlyuchenkova: It hasn't sunk in yet!
'It hasn't sunk in yet!' - Pavlyuchenkova's on-court interview
"It hasn't sunk in yet. I'm still in the match and focusing on the next point," Pavlyuchenkova said in her post-match interview.
"I was thinking that if I take one or two games on her serve that would be amazing because she is the ace queen on the tour so that was my goal, so I was focusing on returning well.
"I also managed to hold on my serve too, so that helped."
Pliskova acknowledged that while the Russian had played well her own performance was nowhere near what she is capable of.
"She was playing very well today. Maybe the best what she played against me so far," Pliskova said.
But let's say I was about 40% today of my game, so of course then she can feel so much better if I just don't play (to the level) what I can play."