The No.3-seeded Azarenka had much bigger leads in both sets, though - she saw a 5-0 first set lead turn into 5-4, then a 4-1 second set lead turn into 4-3 - but every time Beck caught up Azarenka pulled away again, and eventually she was just too powerful on the big points for the young German.
"I think it was very hard conditions today in terms of waiting, and there is so much on, off, on, off - it's not consistently raining or consistently not raining," Azarenka said in her post-match presser. "It was definitely difficult, but it's the same for everybody. So it was just a matter of being patient with it all.
"I felt like I started the match really well, and then after that little break it was a little bit weird, and I came back and felt I really lost my focus there. And she came into the match really aggressive and getting every ball back too. So I lost my focus a little bit, but I'm glad I could turn it around and step it up in the important moments. It was important to close out the first set. I felt it was a good match."
"I'm very happy to reach the third round, but at the same time I'm not surprised - I was expecting this for myself, especially after Strasbourg last week," Cornet said. "This was my goal, reaching the third round, and I was hoping to play Azarenka, maybe on center court. I'm really excited about it."
"I remember playing her in Beijing last year and losing pretty badly," Cornet said. "The conditions were different though - it was a hardcourt, and here it's going to be a totally different surface. And also I was trying to find my forehand at that time there - I was playing totally differently than I am now.
"I know Victoria will be a great challenge for me, but I will be ready. I'll try my best."
"We've played a couple of times and I think she's very talented; we also played together in juniors, so we know each other pretty well," Azarenka said. "I never played against her on clay, so that could be a good challenge. It will be fun, and I think it will definitely be on center court, I'm hoping."
Other seeds in action included No.7 seed Petra Kvitova, who beat Peng Shuai, 64 63; No.16 seed Dominika Cibulkova, who was ousted by Marina Erakovic, 62 26 64; and No.17 seed Sloane Stephens, who continued to find her feet on the clay with a straight set win over countrywoman Vania King, 61 63.
"I've been playing better and better," Stephens said. "It's always tough playing another American, so when I got out there I was a little nervous, but I've been playing well so I was also excited to get out there. I'm just happy to be competing and winning again. Fortunately I played well today."