Serena Williams had to fight back from a set down against teenager Caty McNally.
The 23-time Grand Slam took control midway through the second set on her way to a 5-7 6-3 6-1 victory.
“I think it’s great because I want to be able to win matches where I’m not playing my best, play players who are playing great, be able to come through,” said Williams
“I need to be tested, I guess.”
She added: “Obviously I would be so lying if I said I enjoy the tough matches more, but I think, looking back years later, I enjoy the tough matches more.
“But in the moment, in the weeks after, it’s definitely a different feeling.”
Karolina Muchova, meanwhile, got the better of Su-Wei Hsieh over three sets to book her place in the third round.
This will be Muchova’s first meeting with Williams.
How to live stream Serena Williams vs Karolina Muchova
Fans in the UK can stream the match via Amazon Prime Video.
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For TV information on Williams vs Muchova, head here.