The No.4-seeded Radwanska was never really in trouble in the match, hitting 18 winners to just five unforced errors en route to a one-hour, 21-minute, 62 64 victory over the No.14-seeded Ivanovic.
"I don't know the statistics, but that's for sure one of my best matches of the year for sure, and especially on clay," Radwanska said. "I'm just very happy about it. Everything was working for me.
"I'm very, very happy to reach my first quarterfinal here. It's been great, especially on a surface I didn't really have good results on before, especially this year. So I'm just very excited about this."
"Almost, almost," she said in her presser.
Radwanska's clay court lead-up was the thinnest of any of the top players - she played two events and won one round total. But clearly that hasn't hampered her at the big one this fortnight in Paris.
"Losing early in the tournaments before didn't help, but I'm happy I'm doing better here," Radwanska said. "I'm trying my best, and I'm even playing much better in this match than my first match. Ana played really well today - if I played like in the rounds before, I think I wouldn't make it today."
Ivanovic, who has now lost her last seven meetings with Radwanska, also thought it was high quality.
"I actually think the match was closer than maybe the score indicates," Ivanovic said. "I think maybe it was my serve. If you lose your serve, you know against her you have to win points over and over again, and there's a point where it gets frustrating and you really have to just stick through with it.
"At some points I didn't stick through with it, and that made a big difference today."
Next up for Radwanska is No.5 seed Sara Errani, who beat No.20 seed Carla Suárez Navarro earlier in the day. Radwanska leads Errani in their head-to-head, 6-1, though they haven't played this year yet.
"Sara is a very good clay court player, so for sure it's going to be very tough, especially since she's defending the final here," Radwanska said. "The last match we played - it was Istanbul - we played three and a half hours. I was just better by a few points. It's not like I'm winning easy or anything.
"What I remember most about that match is I couldn't walk the next day."
So her strategy? "I have to prepare for a lot of rallies, a lot of running, and for a close match. And this is a quarterfinal, so it doesn't matter who's on the other side, it's going to be someone good."