The early goings were scratchy - Radwanska went up 2-0, but then Meusburger broke back to catch up to 2-all, and they traded breaks again to get to 3-all. But it was there that the No.1-seeded Radwanska started to pile it on, winning eight of the next nine games to build a 64 50 lead; she got broken while serving for the match but broke the No.6-seeded Meusburger one last time to close it out, 64 61.
"The court was a bit different from that in the first two matches," Radwanska said after the match.
"It took some time before I got used to it, but the most important thing is that I got through."
The court felt different because it was different - overnight, the two main courts were converted into one. See the time lapse video of the transformation here (courtesy of Katowice City Hall)...
The win was Radwanska's 21st WTA-level match win of the year, tying her as the leader with Li Na.
But there was another reason this win was special - very special, indeed.
"One of the things I like most about this tournament is that it's not far from the place where I live, it's like a 45-minute drive away," Radwanska described. "I got really excited when I noticed my beloved grandma Wieslawa beside my mother in the stands. She has always been one of my biggest fans and supporters, she has watched all my matches on TV or internet since the very beginning of my career. But never before had she seen me play live, and now she can come to see all of my matches.
"Her presence gives me positive vibes. I'm so happy!"
Awaiting Radwanska in the semifinals is No.4-seeded Alizé Cornet, who won a surprisingly streaky match against No.5-seeded Klara Koukalova earlier in the day, 62 06 62. After cruising through the first set, Cornet was overpowered in a lopsided 29-minute second set - but she regrouped to win in three.
Radwanska has beaten Cornet in straight sets in all three of their previous meetings, but they've all been close - including their last one just a matter of weeks ago in the fourth round of Indian Wells.
"We've played a couple of good matches in the past," Radwanska said.
"This semifinal match is going to be anything but easy."