The 31-year-old received medical treatment on her ankle after taking a tumble in the fourth game of the first set, before going on to complete an emphatic 6-0 6-0 win.
The four-time Australian Open winner will face Spain’s Garbine Muguruza on Thursday – and Williams is confident that she will be fully fit for the second-round tie.
“I’ll be out there [for the second round]. Unless something fatal happens to me, there’s no way I’m not going to be competing,” said Williams.
“I’m alive. My heart’s beating. I’ll be fine.”
She added: “I’ve been injured before. I’ve played this tournament with so many injuries and was able to come off pretty on top.
“For me it’s just another page and a great story to tell the grandkids one day.”
Williams twisted her ankle in a WTA tournament in Brisbane ahead of last year’s Australian Open, where she lost in the fourth round to Ekaterina Makarova.
And the American admitted Tuesday’s slip reminded of her that injury.
“It reminded me a lot of Brisbane. I thought, ‘Oh, not again’. But, I’ve had such a good year that I don’t think it’s anything negative,” she said.
“I just think that I was definitely a little bit in shock and I was thinking, ‘I hope it’s not as serious’, because it was really serious last year.”
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BIOGRAPHY: Eric Bailly