The Polish world number three took one hour and 44 minutes to end Schiavone's hopes with a 6-4 6-3 win to set up a last-eight encounter with Yvonne Meusburger.
It was far from plain sailing for the top seed though, as former world number four and 2010 French Open champion Schiavone proved a tough customer.
The Italian built a 4-2 lead in the opening set, only to see Radwanska up her play and take seven of the next eight games to pocket the first set and open up a 3-1 lead in the second.
After a series of holds, Radwanska broke once more, decisively, to seal her 20th victory on the WTA Tour this year.
"Francesca already showed that she's in great form here in Katowice when she dropped just two games in her first round match," Radwanska said.
"I expected a tough battle from start to finish, and I got exactly what I expected. She moved so well today that I had to show my best tennis to beat her.
"I'm really happy I managed to close out the match in straight sets.
"It always feels great to get one more win, as any WTA-level match on the road is difficult, and hopefully the season will continue this way for me."
Katowice Open results
7-Magdalena Rybarikova (Slovakia) beat Silvia Soler Espinosa (Spain) 6-2 6-0
6-Yvonne Meusburger (Austria) beat Mirjana Lucic-Baroni (Croatia) 6-2 6-3
1-Agnieszka Radwanska (Poland) beat Francesca Schiavone (Italy) 6-4 6-3
4-Alize Cornet (France) beat Kristina Kucova (Slovakia) 6-3 4-6 6-3
Copa Bogota results
Lara Arruabarrena Vecino (Spain) beat 7-Paula Ormaechea (Argentina) 6-4 7-6(3)
5-Caroline Garcia (France) beat Danka Kovinic (Montenegro) 2-6 6-3 6-4
1-Jelena Jankovic (Serbia) beat Sofia Shapatava (Georgia) 6-4 6-3
Romina Oprandi (Switzerland) beat Irina Begu (Romania) 6-4 6-1
- Sports & Recreation
- Yvonne Meusburger
- Francesca Schiavone