The Czech, who won the Eastbourne without dropping a set in the build up to the tournament at SW19, breezed through the first set in just 20 minutes to complete a bagel.
The Puerto Rican put up more of a defence in the second, only to lose it 6-4.
Pliskova will now face Su-Wei Hsieh.
"I feel like I'm improving every day on grass," said Pliskova, who arrived at Wimbledon full of confidence after scooping her third WTA title on grass at Eastbourne last week.
"The title in Eastbourne helped me feel more confident and to get more used to the surface."
%he third seed appeared to be in the fast lane to victory as she dropped only two points on serve to zoom through the first set.
At the other end of Centre Court, a double fault on set point summed up the kind of torturous day Olympic champion Puig was having to endure.
But just when it seemed the race was on for Pliskova to produce the first double bagel of this year's championships, the Puerto Rican drew a prolonged round of sympathetic applause as she finally won a game in the second game of the second set.
However, her Czech opponent, who could topple Ash Barty from the WTA rankings summit if she reaches the latter stages of the grasscourt major, was not exactly in a charitable mood as she broke Puig to go 3-1 ahead and served for the match at 5-3.
Being on the edge of defeat allowed Puig to come out swinging in the ninth game as she broke Pliskova.
But if that gave Puig a glint of hope for an upset, the Czech quickly snuffed out such thoughts by breaking the 25-year-old in the very next game to seal a third-round match with Taiwanese 28th seed Hsieh Su-wei.
More to follow…