The day belonged to the Radwanska sisters at the Brussels Open as top seed Agnieszka and younger sibling Urszula both won.
The 21-year-old Urszula, who came through qualifying, was dominant against world number eight Bartoli, who did not get the warm-up for next week's French Open she would have wanted as she crashed out 6-4 6-2.
"Of course Marion is a great player, but I was just focusing on my game," Radwanska said on www.wtatennis.com.
"The crowd was really good to me today, it felt like I was at home. The courts are really nice and things have been going well for me. I will just keep trying my best in my next match."
World number three Agnieszka has been one of the form players of the season and she allowed Ukraine's Lesia Tsurenko only one game in a 6-1 6-0 thrashing.
The number one seed next faces Belgian wild card Alison Van Uytvanck, who saw off Chanelle Scheepers 4-6 6-4 6-2, while Urszula will meet Sofia Arvidsson after she benefited from the retirement of Arantxa Rus with a back injury.
Fourth seed Dominika Cibulkova advanced to the last eight with a 6-3 6-4 victory over home hope Yanina Wickmayer but Russia's Nadia Petrova, the 10th seed, lost 6-3 6-2 to Tsvetana Pironkova.
There were also wins today for eighth seed Kaia Kanepi, who defeated Bojana Jovanovski 6-2 6-2, and Simona Halep, a 6-1 6-1 victor over fellow Romanian Monica Niculescu.
