The No.14-seeded Ivanovic had won the pair's last four meetings and this one wasn't too different, as she was just too dangerous on her forehand and too sharp in every other part of her game too.
"It's a good feeling, especially because I feel like each match I've been playing better," Ivanovic said. "I was really happy with my performance today because I knew Virginie is a tough opponent, and she can be very streaky. So I'm very happy with how I handled it and happy with the end result of course."
Razzano, a former Top 20 player and always classy, was gracious in defeat to the former World No.1.
"Losing is never fun, but she was playing too well today - when she's playing well you just don't have time to play," Razzano said. "I've missed playing against this pace and this rhythm. It's been a long time since I played against a top player, several months at least. So I will need to go back and work on my game to feel comfortable with it again, and fight against players like Ana again in the future.
"But at the end of the day, three months ago I couldn't have believed I would reach third round at Roland Garros. It's wonderful. I'm proud. I'm very happy. I hope for more, but I'm very satisfied with what I've done here this week, what I've accomplished. And I'll still work really, really, really hard to improve and get back to this level. I know I'll get it back up there soon; I'll be even better."
Ivanovic is through to the second week for the fourth Grand Slam in a row - she got to the fourth round of Wimbledon (falling to Victoria Azarenka), the quarterfinals of the US Open (falling to Serena Williams) and the fourth round at the Australian Open (losing to Agnieszka Radwanska).
"I always feel like I get to the fourth round or quarterfinals and then play a Top 10 player, or a Top 5 player - so nothing is going to be different this time around if Radwanska wins," Ivanovic said. "But I think it's about time to make this step and actually be the Top 10 player. That's my big goal."
The No.4-seeded Radwanska did end up holding her end of the bargain, beating German qualifier Dinah Pfizenmaier in straight sets in the last match of the day on Court Philippe Chatrier, 63 64.
"First of all I'm just happy I finished the match, especially because it was quite tough, especially in the end of the second set, 4-3 down and break points down as well," Radwanska said. "I also knew it was getting dark. It was after 9 o'clock. I saw the clock over on the side of the court. I just wanted to finish the match so badly - I think it was a good motivation and I'm happy it worked out in the end."
Radwanska's sister, Urszula Radwanska, had lost to Pfizenmaier in the last round. "She told me a couple of tips about her, especially since I didn't know her before," Radwanska said. "I didn't see their match because I played the same time as them. But I think it was good to avenge my sister."
Radwanska leads Ivanovic in their head-to-head series, 6-3, but perhaps more worrying for Ivanovic is Radwanska has won their last six meetings in a row - Ivanovic won their first three meetings.
"Obviously I know Radwanska very well," Ivanovic said. "We played each other a couple times this year already and in the past a few times, so I know what to expect. She's so consistent, but she's also not afraid to come in. She likes to use drop shots and she moves really well too. She makes you win the points over and over again. I need to be patient - that will be a very big key against her."
Other winners were No.5 seed Sara Errani, who beat No.32 seed Sabine Lisicki, 60 64; No.8 seed Angelique Kerber, who beat No.29 seed Varvara Lepchenko for the first time in five meetings, 64 67(3) 64; No.15 seed Roberta Vinci, who beat Petra Cetkovska, 61 26 62; No.20 seed Carla Suárez Navarro, who beat Monica Puig, 64 75; and Svetlana Kuznetsova, who beat Bojana Jovanovski, 64 76(2).