Peer has had a legendary career - highest-ranked Israeli ever, even getting to within one spot of becoming her country's first Top 10 player. But she has had something of a drought recently - before this week she had reached 44 WTA quarterfinals, but she hadn't gone that deep since January 2012.
All of that changed on Thursday as Peer, who got into this week's main draw as a lucky loser and battled over three hours to win her first round match, blazed past Jill Craybas in straight sets in her second round match, breaking serve six times to beat the veteran American qualifier, 61 63.
"First of all I'm really happy because every match I'm playing much, much better," Peer said after reaching her 45th WTA quarterfinal. "From the first round of qualies to first round of main draw was already much better, and today I played well the whole match, so I'm happy about my performance.
"Jill and I both came from the qualifying so we both had a lot of matches. She's a good player with a lot of experience, and I lost to her a few years ago, so at least this time I won against her."
Two of the five WTA titles Peer has won were on clay, but her favorite surface is hard - that's what the other three titles came on and that's also what both of her Grand Slam quarterfinals came on.
"I'm still getting used to the clay," Peer commented. "I don't come from a clay background so it takes me a while to get used to it each year, but when I play well, I play well. And that's it, really."
"My next opponent is another qualifier, so this tournament is really a good one for qualifiers," Peer said. "I saw a bit of her match against Begu earlier in the day and she was playing really, really well.
"I will just have to play well again and we'll see what happens tomorrow."
Peer and Cadantu will be playing against each other for the first time.
Also winning through earlier in the day was No.2 seed Roberta Vinci, who was overpowered in the first set but battled back to beat Kiki Bertens in three sets, 26 63 64, saving her best for the most important moment in the match - she grabbed the critical break of serve at 4-all in the third and served it out.
"I started slow - when I lost the first set I decided to play more aggressive and go up to the net more," Vinci said. "I definitely played better tennis at the end, more consistent and more focused too."
Next up for Vinci is a first-time meeting against Czech wildcard Karolina Pliskova.
"I started pretty slowly on the court and she was playing quite well, she didn't have as many mistakes as me," Kvitova said. "That was the key to get back - just to play at ease and not have as many mistakes as I had at the beginning. Also just keep my serve and wait for my moment to break her."
Next up for Kvitova will be Petra Martic - and Martic actually won the pair's only previous meeting, a straight set second round upset in Tokyo last fall, her first Top 5 win over the No.5 at the time.
"I played her in my first round in Tokyo and I lost," Kvitova said. "I know how she plays - she plays so fast and very aggressively, and she has a good serve, so I think it will be a very tough match.
"I hope revenge can come tomorrow."