Poland's Swiatek, who has put together the longest winning run since Serena Williams racked up 27 victories in 2015, will face 2019 U.S. Open champion Bianca Andreescu in the quarter-finals of the claycourt event on Friday.
Swiatek, the 2020 French Open champion, is seeking her fifth title this season, having won in Doha, Indian Wells, Miami and Stuttgart.
Andreescu reached her first WTA 1000 quarter-final in 14 months by defeating qualifier Petra Martic 6-4 6-4.
Third seed Aryna Sabalenka defeated Jessica Pegula 6-1 6-4 to reach the Rome last eight for the first time.
Photo: PHOTOSPORT Caption: World number one Iga Swiatek