The No.1-seeded Radwanska held all nine of her service games and broke Pliskova's serve three times - including twice at love - to roll past the Czech wildcard in an hour and nine minutes, 63 62.
Radwanska's serve was particularly strong - she hit five aces, including three in a row at one point.
"It's always hard to play against a lefty big-server like Kristyna, who is very talented and never gives you too much rhythm," Radwanska said. "I had to play very well today to win this match."
This is the third time Radwanska is playing a WTA event in Poland. The first two times came at Warsaw in 2006 and 2007 - when she played there in 2006 it was actually her first WTA main draw.
"The BNP Paribas Katowice Open is my third WTA tournament back home in my career and I must say that I'm really excited," the World No.3 commented. "I still have vivid memories of my first ever WTA main draw event at the Premier event in Warsaw in 2006. As a 17-year-old girl, I managed to beat 2004 French Open champion Anastasia Myskina in the first round. I couldn't imagine a better debut! After winning my second round match, I lost to Elena Dementieva in the quarterfinals in three sets.
"So my tennis career really began in my home country and I'm thankful for this opportunity."
In 2007, Radwanska reached the second round in Warsaw, falling in three sets to Alona Bondarenko.
Katowice is hosting an International-level event, but the field is still very strong - Radwanska is joined by her fellow Top 20 players Roberta Vinci and Carla Suárez Navarro, as well as former Top 20 players Francesca Schiavone, Alizé Cornet, Shahar Peer, Yanina Wickmayer and Klara Koukalova.
"It's great to see such a strong field here in Katowice this week," Radwanska said. "There are so many Top 20 players. It's also good for my country to have a tournament like this, and it's good for our young Polish players too - I hope some of them will have a breakthrough themselves this week."
Radwanska is now 19-6 in 2014 and will go for her 20th match win of the year in her next match.