Stosur and Li were both first match on and it was the No.6-seeded Li who got to the finish line first, blasting 29 winners to 12 unforced en route to a 67-minute, 61 61 victory over Michaella Krajicek.
"It's a pretty good start for me here," Li said. "The last two years I wasn't doing well on grass, I was shocked a little bit, so that's why I asked for a wildcard at Eastbourne a week ago. I have to get used to playing on the grass more. And I was actually feeling pretty happy with my game on the court."
The No.14-seeded Stosur needed just three more minutes to complete a 61 63 win over Slovakian lucky loser Anna Schmiedlova, compiling an almost-as-impressive winners-to-errors ratio of 25 to 10.
"I didn't know too much about her but I did know a few little things, which I tried to take advantage of early on," Stosur said. "Then once I felt like I was in control of what was going on, I tried a few serve-volleys, kept trying to move forward, and just playing the way I want to keep playing on grass."
"My first thought when I saw the draw was it won't be easy to play against her in the first round; the second thing I was thinking was that I had never beaten her before," Kerber said. "But I was talking with my coach a little bit and he just told me I've been playing very well on grass, he reminded me I love to play on grass, and I had never played against her before on grass, so that was my hope today."
Kerber has been to two Grand Slam semifinals before - the US Open in 2011 and right here last year. She was asked about the memories she had from last year's run. "I have great memories from last year, but I'm not thinking about defending points, losing points or winning points - it doesn't matter to me. It's just a new year. I'm here like any other person, except this year I'm No.7 or No.8 seeded."
The other Top 10 players in action had mixed results, with No.1 seed Serena Williams cruising past Mandy Minella (read more here), No.4 seed Agnieszka Radwanska routing Austrian qualifier Yvonne Meusburger, 61 61, but No.10 seed Maria Kirilenko falling to Laura Robson (read more here).
There were a few other upsets, with Karolina Pliskova surprising No.13 seed Nadia Petrova, 63 62, Tsvetana Pironkova stunning No.21 seed Anastasia Pavlyuchenkova, 60 61, and Alexandra Cadantu beating No.28 seed Tamira Paszek, 62 75. All three seeds have been to the quarters or better here.
Also, No.31 seed Romina Oprandi had to retire in the third set of her match against American wildcard Alison Riske due to a right forearm injury. She was behind 3-1 in the third set when she had to stop.
Other seeds moving on were Roberta Vinci, Dominika Cibulkova, Sabine Lisicki, Peng Shuai, Mona Barthel and Klara Zakopalova. The No.30-seeded Barthel had by far the closest call, coming back from triple match point down serving 4-5, 0-40 in the third set to beat Monica Niculescu, 63 46 75.