"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."
But if Pliskova was hoping her success at Eastbourne would easily translate to a Wimbledon title, she will have to buck recent trends as fellow Czech Jana Novotna was the last woman to have pulled off the feat 21 years ago.
On Wednesday, though, Pliskova showed why she is considered as one of the front runners for this year's Wimbledon crown.
Watched on by former Formula One driver David Coulthard from the Royal Box, the 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 in 20 minutes.
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.
"The deeper you go, the better players you play so it's not going to be easy here," said Pliskova, whose only defeat on grass this season was against her twin Kristyna in the last 16 in Birmingham.
Pliskova is one of four former WTA number ones in action on Wednesday. Belarussian Victoria Azarenka was even more ruthless than Pliskova as she dished out a 6-2 6-0 mauling to Ajla Tomljanovic while Simona Halep and Caroline Wozniacki will be in action later on day three of the championships.