After falling to Ekaterina Makarova in straight sets in the fourth round of the Australian Open, Kerber also fell in straight sets in her opening matches at both events since - to Mona Barthel in Doha and Roberta Vinci in Dubai - but the No.4-seeded German turned the tide in a very big way Saturday, breaking serve five times and needing just 67 minutes to breeze past Irina-Camelia Begu, 63 62.
Kerber and Wickmayer are tied in their head-to-head, 1-1, both meetings being tough three-setters.
"Madison's got a big game - obviously her forehand is massive and she's got a very big serve," Stosur said afterwards. "She's got a pretty decent kick serve for a second serve, too, and handled a lot of my slice quite well sometimes. She's just got to put all the pieces together - she's only 18 years old, and I had lots of pieces like that when I was 18 and wasn't as together as probably what she is now.
"I think she's got a lot of potential. She has those big weapons that win those big matches."
Despite playing one of the home players, Stosur was warmly cheered on by the Indian Wells crowd.
"I have always had great support here in America - not just here, but in American in general," Stosur said. "I think maybe part of that is from my doubles back in the day with Lisa - they got to know me a little bit, and obviously since I won the US Open, as well. It's one of those places I feel comfortable playing. I always have good support no matter who I'm playing. It was a good crowd today."
And despite not coming out on the winning end, Keys was happy with the experience of playing Stosur.
"I think if I was returning better today, maybe I could have made the match a little bit tighter, but it's such a great learning experience," Keys said. "There are some things I need to work on now, especially my returns. So I'll go back, work on those, and, you know, move onto the next tournament."
Keys pointed to one thing as the biggest difference between herself and the top players. "I think they do such a great job under pressure," she said. "Like there were times when it was 30-all on her serve and she would make her first serve and have a forehand - and on the other side, I would miss my first serve and get super nervous on the second serve. So they play the right shots on important points."
Other seeds moving through earlier in the day were No.10 seed Nadia Petrova, No.21 seed Julia Goerges, No.28 seed Kirsten Flipkens and No.32 seed Peng Shuai. There was a pair of upsets, with Spanish qualifier Garbiñe Muguruza rallying from a break down twice in the third set to beat No.17 seed Ekaterina Makarova, 63 16 64, and Jamie Hampton beating No.20 seed Hsieh Su-Wei, 63 63.
"She's pretty tricky, talented, has good hands," Hampton said of Hsieh. "With any two-hander, probably stretch them a little bit to their cross hand, try to play up the middle, jam them a bit and not give them the angles, because you could see when I did give her the angle it was some good tennis."